def _design(self):
if not self.stopband_attenuation and 'stopband_attenuation' in self.filter_parameters:
self.stopband_attenuation = self.filter_parameters['stopband_attenuation']
elif not self.stopband_attenuation and 'stopband_attenuation' not in self.filter_parameters:
raise ValueError("Needs a stopband_attenuation value.")
if self.already_normalized_Wn:
self.Z, self.P, self.K = signal.cheby2(self.N, self.stopband_attenuation, self.Wn,
self.filter_kind, analog=False,
output='zpk')
else:
self.Z, self.P, self.K = signal.cheby2(self.N, self.stopband_attenuation, self.normalize_Wn(),
self.filter_kind, analog=False,
output='zpk')
def lowpass_cheby_2(data, freq, df, maxorder=12, ba=False,
freq_passband=False):
"""
Cheby2-Lowpass Filter
Filter data by passing data only below a certain frequency.
The main purpose of this cheby2 filter is downsampling.
#318 shows some plots of this filter design itself.
This method will iteratively design a filter, whose pass
band frequency is determined dynamically, such that the
values above the stop band frequency are lower than -96dB.
:type data: numpy.ndarray
:param data: Data to filter.
:param freq: The frequency above which signals are attenuated
with 95 dB
:param df: Sampling rate in Hz.
:param maxorder: Maximal order of the designed cheby2 filter
:param ba: If True return only the filter coefficients (b, a) instead
of filtering
:param freq_passband: If True return additionally to the filtered data,
the iteratively determined pass band frequency
:return: Filtered data.
"""
nyquist = df * 0.5
# rp - maximum ripple of passband, rs - attenuation of stopband
rp, rs, order = 1, 96, 1e99
ws = freq / nyquist # stop band frequency
wp = ws # pass band frequency
# raise for some bad scenarios
if ws > 1:
ws = 1.0
msg = "Selected corner frequency is above Nyquist. " + \
"Setting Nyquist as high corner."
warnings.warn(msg)
while True:
if order <= maxorder:
break
wp = wp * 0.99
order, wn = cheb2ord(wp, ws, rp, rs, analog=0)
if ba:
return cheby2(order, rs, wn, btype='low', analog=0, output='ba')
z, p, k = cheby2(order, rs, wn, btype='low', analog=0, output='zpk')
sos = zpk2sos(z, p, k)
if freq_passband:
return sosfilt(sos, data), wp * nyquist
return sosfilt(sos, data)
def zerophase_chebychev_lowpass_filter(trace, freqmax, verbose, ofid=None):
"""
Custom Chebychev type two zerophase lowpass filter useful for decimation
filtering.
This filter is stable up to a reduction in frequency with a factor of 10.
If more reduction is desired, simply decimate in steps.
Partly based on a filter in ObsPy.
:param data: Input trace
:param freqmax: The desired lowpass frequency.
Will be replaced once ObsPy has a proper decimation filter.
"""
# rp - maximum ripple of passband, rs - attenuation of stopband
rp, rs, order = 1, 96, 1e99
ws = freqmax / (trace.stats.sampling_rate * 0.5) # stop band frequency
wp = ws # pass band frequency
while True:
if order <= 12:
break
wp *= 0.99
order, wn = cheb2ord(wp, ws, rp, rs, analog=0)
b, a = cheby2(order, rs, wn, btype="low", analog=0, output="ba")
# Apply twice to get rid of the phase distortion.
trace.data = filtfilt(b, a, trace.data)
def add_antialias(self,Fs,freq,maxorder=8):
# From obspy
nyquist = Fs * 0.5
# rp - maximum ripple of passband, rs - attenuation of stopband
rp, rs, order = 1, 96, 1e99
ws = freq / nyquist # stop band frequency
wp = ws # pass band frequency
# raise for some bad scenarios
if ws > 1:
ws = 1.0
msg = "** Selected corner frequency is above Nyquist. " + \
"** Setting Nyquist as high corner."
warnings.warn(msg)
while True:
if order <= maxorder:
break
wp = wp * 0.99
order, wn = cheb2ord(wp, ws, rp, rs, analog=0)
z, p, k = cheby2(order, rs, wn,
btype='low', analog=0, output='zpk')
self.anti_alias = zpk2sos(z,p,k)
return()
def add_lfp(spike_entry, raw_entry, Nlfp, cutoff=300, order=4,
ripple=20, lfp_sampling_rate=1000, verbose=True):
"""adds first N lfp channels to the spike_entry"""
data_channels = [x for x in raw_entry.values()
if isinstance(x, h5py.Dataset)
and 'datatype' in x.attrs
and int(x.attrs['datatype']) < 1000]
print(len(data_channels))
data_channels = sorted(data_channels, key=repr)[:Nlfp]
for chan in data_channels:
if verbose:
print("lfp chan: {}".format(chan))
# low pass filter
b, a = cheby2(order, ripple,
cutoff / (chan.attrs['sampling_rate'] / 2.))
lfp = filtfilt(b, a, chan)
# resample
old_x = np.arange(len(chan)) / chan.attrs['sampling_rate']
resample_ratio = chan.attrs['sampling_rate'] / lfp_sampling_rate
new_x = np.arange(len(chan) / resample_ratio) / lfp_sampling_rate
resamp_lfp = np.interp(new_x, old_x, lfp)
arf.create_dataset(spike_entry, chan.name, resamp_lfp,
units='samples', datatype=2,
sampling_rate=lfp_sampling_rate)
def lowpass_cheby2_coeffs(freq, sr, maxorder=12):
# type: (float, int, int) -> Tuple[np.ndarray, np.ndarray, float]
"""
freq : The frequency above which signals are attenuated
with 95 dB
sr : Sampling rate in Hz.
maxorder: Maximal order of the designed cheby2 filter
Returns --> (b coeffs, a coeffs, freq_passband)
"""
nyquist = sr * 0.5
# rp - maximum ripple of passband, rs - attenuation of stopband
rp, rs, order = 1, 96, 1e99
ws = freq / nyquist # stop band frequency
wp = ws # pass band frequency
# raise for some bad scenarios
if ws > 1:
ws = 1.0
msg = "Selected corner frequency is above Nyquist. " + \
"Setting Nyquist as high corner."
warnings.warn(msg)
while True:
if order <= maxorder:
break
wp = wp * 0.99
order, wn = signal.cheb2ord(wp, ws, rp, rs, analog=0)
b, a = signal.cheby2(order, rs, wn, btype='low', analog=0, output='ba')
return b, a, wp*nyquist
def __init__(self, frequency, band):
"""
"""
fn = frequency / 2.0
b, a = cheby2(1, 10, np.array(band)/ fn, btype = "bandpass")
self.b = b
self.a = a
def HPmin(self, fil_dict):
self._get_params(fil_dict)
self.N, self.F_SBC = cheb2ord(self.F_PB, self.F_SB,self.A_PB,self.A_SB,
analog=self.analog)
if not self._test_N():
return -1
self._save(fil_dict, sig.cheby2(self.N, self.A_SB, self.F_SBC,
btype='highpass', analog=self.analog, output=self.FRMT))
def BSmin(self, fil_dict):
self._get_params(fil_dict)
self.N, self.F_SBC = cheb2ord([self.F_PB, self.F_PB2],
[self.F_SB, self.F_SB2], self.A_PB, self.A_SB, analog=self.analog)
if not self._test_N():
return -1
self._save(fil_dict, sig.cheby2(self.N, self.A_SB, self.F_SBC,
btype='bandstop', analog=self.analog, output=self.FRMT))
def __init__(self, frequency, threshold):
"""
"""
fn = frequency / 2.0
b, a = cheby2(1, 10, threshold / fn, btype = "lowpass")
self.b = b
self.a = a
def decode_efm(apply_filters=True, apply_demp=False, just_log=True, random_input=False):
""" Decode EFM from STDIN, assuming it's a 28Mhz 8bit raw stream.
apply_filters apply lowpass/highpass filters
apply_demp apply de-emphasis filter (False for CD Audio)
just_log just log to stderr, don't bother decoding
random_input run against white noise"""
if random_input:
data = np.random.random_integers(-10000, 10000, SAMPLES)
else:
data = np.fromstring(sys.stdin.read(SAMPLES), dtype=np.uint8).astype(np.int16)
data = sps.detrend(data, type='constant') # Remove DC
data = auto_gain(data, 10000, 'pre-filter') # Expand before filtering, since we'll lose much of signal otherwise
if apply_demp:
# This is too slow, need to work out a way to do it in scipy
de_emphasis_filter = biquad_filter(-1.8617006585639506, 0.8706642683920058, 0.947680874725466,
-1.8659578411373265, 0.9187262110931641)
data = np.fromiter(run_filter(de_emphasis_filter, data), np.int16) # De-emph - 26db below 500khz
if apply_filters:
# bandpass = sps.firwin(8191, [0.013 / FREQ_MHZ, 2.1 / FREQ_MHZ], pass_zero=False)
# data = sps.lfilter(bandpass, 1, data)
low_pass = sps.cheby2(16, 100., 4.3 / FREQ_MHZ) # Looks a bit odd, but is a reasonable tie for the spec filter (-26db at 2.0 Mhz, -50+ at 2.3Mhz)
# low_pass = sps.cheby2(10, 50., 4.3 / FREQ_MHZ) # Looks a bit odd, but is a reasonable tie for the spec filter (-26db at 2.0 Mhz, -50+ at 2.3Mhz)
data = sps.filtfilt(low_pass[0], low_pass[1], data)
bit_gen = edgeclock_decode(data, 0., 6.626)
data_frames = []
try:
frame_bytes = []
frames = 0
while 1:
if just_log:
printerr([ bit_gen.next(), bit_gen.next(),bit_gen.next(),bit_gen.next(),bit_gen.next(),bit_gen.next(),bit_gen.next(),bit_gen.next(),bit_gen.next(),bit_gen.next(),bit_gen.next(),bit_gen.next(),bit_gen.next(),bit_gen.next()])
else:
run_until_start_code(bit_gen)
consume_merging_bites(bit_gen)
frames += 1
frame_bytes.append(list(consume_f3_frame(bit_gen))) # 31 14 bit EFM codes in a frame
if len(frame_bytes) == EFM_FRAME_LENGTH:
f2frame = consume_f2_frame(frame_bytes)
data_frames.append(consume_f1_frame(f2frame))
frame_bytes = []
#
except StopIteration:
printerr('Hit the end of the bitstream')
printerr('Found %d frames ' % frames)
printerr(' Expected %.2f frames' % ((SAMPLES / 6.626 ) / 588 ))
## Output data should now contain all the decoded frames
audioleft, audioright = extract_audio_samples(data_frames)
data = np.clip(data, 0, 255).astype(np.uint8)
sys.stdout.write(data.tostring())
def cheby2_lowpass_filter(_data, _frequency_cutoff, _carrier_frequency, order):
"""
:param _data: The data to be lowpassed
:param _frequency_cutoff: The frequency cutoff for the filter
:param _carrier_frequency: The carrier frequency for the filter
:param order: The order of the filter
:return: The output of the lowpass filter (entire window)
"""
nyq = 0.5 * _carrier_frequency
low = _frequency_cutoff / nyq
b, a = signal.cheby2(order, 5, low, 'low', analog=False, output='ba')
return signal.lfilter(b, a, _data)
def cheby2_highpass_test(): import numpy as np from numpy.testing import assert_almost_equal from scipy.signal import cheby2 x = np.arange(10000).reshape(1, -1) d = np.sin(x * 2 * np.pi * 1000 / 48000) out, b, a = filter_high(d) bref, aref = cheby2(5, 3, 1000/24000., btype='highpass') assert_almost_equal(-b, bref) assert_almost_equal(np.hstack(([1], -a[::-1])), aref)
def _NOTCH_Cheby2_bandstop(interval, sampling_rate, cutoff, order=5):
nyq = sampling_rate * 0.5
stopfreq = float(cutoff) + 300.0
cornerfreq = float(cutoff) - 300.0
Ws = stopfreq / nyq
Wp = cornerfreq / nyq
# N, Wn = cheb2ord(Wp, Ws, 3, 60) # (?)
N, Wn = cheb2ord([0.3, 0.5], [0.45, 0.48], 3, 160) # (?)
# print N, Wn, Wp, Ws, stopfreq, cornerfreq
b, a = cheby2(N, 60, Wn, btype="stop") # should 'high' be here for bandpass?
sf = lfilter(b, a, interval)
return sf, b, a
def iir_basic(a):
filt_type = a["Response Type"]
print('filt_type', filt_type)
design_method = a["Design_Methode"]
if design_method == 'Elliptic':
ftype = 'ellip'
elif design_method == 'Chebychev 1':
ftype = 'cheby1'
elif design_method == 'Chebychev 2':
ftype = 'cheby2'
elif design_method == 'Butterworth':
ftype = 'butter'
# else: raise_exception
print('design_method', design_method)
N = a['Order']
print('order',N)
fs = a["Fs"]
F_pass = 2 * a["Fpass"]/fs
# F_stop = 2 * a[3][2][2]/fs
F_stop = 0.8
print('fs','fpass','fstop',fs, F_pass, F_stop)
A_pass = a["Apass"]
A_stop = a["Astop"]
# A_stop = a[4][2][2]
print('A_pass', 'A_stop', A_pass, A_stop)
# W = a[5]
# print('W',W)
if N == 'min':
b,a = sig.iirdesign(F_pass, F_stop, A_pass, A_stop, analog = False,
ftype = ftype, output = 'ba')
else:
if ftype == 'ellip':
b,a = sig.ellip(N, A_pass, A_stop, [F_pass, F_stop], btype ='low' )
elif ftype == 'cheby1':
b,a = sig.cheby1(N, A_pass, [F_pass, F_stop], btype ='low' )
elif ftype == 'cheby2':
b,a = sig.cheby2(N, A_stop, [F_pass, F_stop], btype ='low' )
elif ftype == 'butter':
b,a = sig.butter(N, (2 * a["Fc"]/fs), btype ='low' )
return b, a
def design(self, ripple=None):
if self.filter_class == 'butterworth':
self.B, self.A = signal.butter(self.N, self.Wn,
self.filter_type, analog=True,
output='ba')
elif self.filter_class == 'chebyshev_1':
if ripple is None or ripple <= 0:
raise ValueError("Must give a ripple that is > 0")
self.B, self.A = signal.cheby1(self.N, ripple, self.Wn,
self.filter_type, analog=True,
output='ba')
elif self.filter_class == 'chebyshev_2':
self.B, self.A = signal.cheby2(self.N, self.stopband_attenuation, self.Wn,
self.filter_type, analog=True, output='ba')
elif self.filter_class == 'elliptical':
self.B, self.A = signal.ellip(self.N, self.passband_attenuation,
self.stopband_attenuation, self.Wn,
self.filter_type, analog=True, output='ba')
elif self.filter_class == 'bessel':
self.B, self.A = signal.bessel(self.N, self.Wn, self.filter_type, analog=True)
else:
raise NotImplementedError("Computation of {} not implemented yet.".format(self.filter_class))
def montage(self, name, type='linkedears', filtr='high', start=None, stop=None, mixed=False):
if filtr:
[b,a] = butter(3,1.0/(self.samplingFrequency()/2.0), btype='high')
if filtr == 'alpha':
Wn = [8.5/(128/2.0),14.5/(128/2.0)]
[g,h] = cheby2(4, 20, Wn, btype='bandpass', analog=0, output='ba')
if type == 'linkedears':
s = self.channel(name, 'name')
#s = filtfilt(b,a,s - (self.channel('A1', 'name') + self.channel('A2', 'name'))/2)
if start and stop:
t = filtfilt(b,a,s[start:stop] - (self.channel('A1', 'name')[start:stop] + self.channel('A2', 'name')[start:stop])/2)
if filtr == 'alpha': t = filtfilt(g,h,t)
elif stop:
t = filtfilt(b,a,s[:stop] - (self.channel('A1', 'name')[:stop] + self.channel('A2', 'name')[:stop])/2)
if filtr == 'alpha': t = filtfilt(g,h,t)
elif start:
t = filtfilt(b,a,s[start:] - (self.channel('A1', 'name')[start:] + self.channel('A2', 'name')[start:])/2)
else:
t = filtfilt(b,a,s - (self.channel('A1', 'name') + self.channel('A2', 'name'))/2)
if filtr == 'alpha': t = filtfilt(g,h,t)
if mixed: t = self.mixer(t)
return t
def __init__(self, filter_type, filter_order, filter_freq, filter_direction, filter_atten=0): """Return a FilterTools object of type *filter_type* as 0 == cheby2 or 1 == butter of order *filter_order* with minimum attenuation *filter_atten* (for cheby2). *filter_freq* is the normalized cutoff frequency 2*fc/fs and *filter_direction* a string determining 'high' or 'low' pass behavior. """ # Handle exceptions # http://stackoverflow.com/questions/2525845/proper-way- # in-python-to-raise-errors-while-setting-variables if(filter_type==0): self.b, self.a = sig.cheby2(filter_order, filter_atten, filter_freq, filter_direction, analog=False, output='ba') elif(filter_type==1): self.b, self.a = sig.butter(filter_order, filter_freq, filter_direction, analog=False, output='ba') self.filter_order = filter_order
def __init__(self, outputConfig, frequency_hz, bw_hz=1e6):
'''
Initialize filter object.
Parameters
----------
outputConfig : object
Output configuration parameters object
frequency_hz : float
Intermediate frequency in hertz
bw_hz : float, optional
Noise bandwidth in hertz
'''
super(BandPassFilter, self).__init__(3., 40.)
self.bw_hz = bw_hz
self.frequency_hz = frequency_hz
passBand_hz = bw_hz
stopBand_hz = bw_hz * 1.2
mult = 2. / outputConfig.SAMPLE_RATE_HZ
order, wn = cheb2ord(wp=[(frequency_hz - passBand_hz) * mult,
(frequency_hz + passBand_hz) * mult],
ws=[(frequency_hz - stopBand_hz) * mult,
(frequency_hz + stopBand_hz) * mult],
gpass=self.passBandAtt_dbhz,
gstop=self.stopBandAtt_dbhz,
analog=False)
b, a = cheby2(order + 1, # Order of the filter
# Minimum attenuation required in the stop band in dB
self.stopBandAtt_dbhz,
wn,
btype="bandpass",
analog=False,
output='ba')
self.a = a
self.b = b
self.zi = lfiltic(self.b, self.a, [])
def __init__(self, outputConfig, frequency_hz=0.0):
"""
Initialize filter object.
Parameters
----------
outputConfig : object
Output configuration parameters object
frequency_hz : float
Intermediate frequency
"""
super(LowPassFilter, self).__init__(3.0, 40.0)
self.bw_hz = 1e6
passBand_hz = frequency_hz + self.bw_hz
stopBand_hz = frequency_hz + self.bw_hz * 1.2
nyqFreq_s = 2.0 / outputConfig.SAMPLE_RATE_HZ # 1.0 /Nyquist frequency
wp = passBand_hz * nyqFreq_s
ws = stopBand_hz * nyqFreq_s
order, wn = cheb2ord(wp=wp, ws=ws, gpass=self.passBandAtt_dbhz, gstop=self.stopBandAtt_dbhz, analog=False)
self.order = order
self.wn = wn
b, a = cheby2(
order + 1, # Order of the filter
# Minimum attenuation required in the stop band in dB
self.stopBandAtt_dbhz,
wn,
btype="lowpass",
analog=False,
output="ba",
)
self.a = a
self.b = b
self.zi = lfiltic(self.b, self.a, [])
def beam_profile_filter_chebyshev(n_macroparticles, resolution, n_slices,
filter_option):
'''
*This routine is filtering the beam profile with a type II Chebyshev
filter. The input is a library having the following structure and
informations:*
filter_option = {'type':'chebyshev', 'pass_frequency':pass_frequency,
'stop_frequency':stop_frequency,'gain_pass':gain_pass,
'gain_stop':gain_stop}
*The function returns nCoefficients, the number of coefficients used
in the filter. You can also add the following option to plot and return
the filter transfer function:*
filter_option = {..., 'transfer_function_plot':True}
'''
import matplotlib as mpl
mpl.use('Agg')
import matplotlib.pyplot as plt
# import os
from scipy.signal import cheb2ord, cheby2, filtfilt, freqz
from numpy.fft import fftfreq, fft
noisyProfile = np.array(n_macroparticles, dtype=float)
freqSampling = 1 / resolution
nyqFreq = freqSampling / 2.
frequencyPass = float(filter_option['pass_frequency']) / nyqFreq
frequencyStop = float(filter_option['stop_frequency']) / nyqFreq
gainPass = float(filter_option['gain_pass'])
gainStop = float(filter_option['gain_stop'])
# Compute the lowest order for a Chebyshev Type II digital filter
nCoefficients, wn = cheb2ord(frequencyPass, frequencyStop, gainPass,
gainStop)
# Compute the coefficients a Chebyshev Type II digital filter
b, a = cheby2(nCoefficients, gainStop, wn, btype='low')
# NOTE 2 lines of code have been commented out!!
# Apply the filter forward and backwards to cancel the group delay
# macroparticles = filtfilt(b, a, noisyProfile)
# macroparticles = np.ascontiguousarray(macroparticles)
# print "n_macroparticles: ", macroparticles
if 'transfer_function_plot' in filter_option and \
filter_option['transfer_function_plot'].lower() == "true":
# Plot the filter transfer function
w, transferGain = freqz(b, a=a, worN=n_slices)
transferFreq = w / np.pi * nyqFreq
group_delay = - \
np.diff(-np.unwrap(-np.angle(transferGain))) / - \
np.diff(w*freqSampling)
plt.figure()
ax1 = plt.subplot(311)
plt.plot(transferFreq, 20 * np.log10(abs(transferGain)))
plt.ylabel('Magnitude [dB]')
plt.subplot(312, sharex=ax1)
plt.plot(transferFreq, np.unwrap(-np.angle(transferGain)))
plt.ylabel('Phase [rad]')
plt.subplot(313, sharex=ax1)
plt.plot(transferFreq[:-1], group_delay)
plt.ylabel('Group delay [s]')
plt.xlabel('Frequency [Hz]')
plt.savefig("filter_transfer_function.png")
plt.clf()
# Plot the bunch spectrum and the filter transfer function
plt.figure()
plt.plot(np.fft.fftfreq(n_slices, resolution),
20 * np.log10(np.abs(np.fft.fft(noisyProfile))))
plt.xlabel('Frequency [Hz]')
plt.twinx()
plt.plot(transferFreq, 20 * np.log10(abs(transferGain)), 'r')
plt.xlim(0, plt.xlim()[1])
plt.savefig("bunch_spectrum_filter_tranfer_function.png")
plt.clf()
res = np.array([nCoefficients], dtype=float)
res = np.append(res,
[transferFreq, transferGain.real, transferGain.imag])
# print n_slices
# print res.shape
return res
else:
# print "I am about to return"
res = np.array([nCoefficients], dtype=float)
res = np.append(res, [b, a])
# print res
return res
def test_cheby2_7(self):
# Test case for analog filter
IIR = IIRDesign.cheby2(self.n, self.Rs, self.Wss, zs='s')
iir = signal.cheby2(self.n, self.Rs, self.Wss, analog=True)
self.assertTrue((IIR[0] == iir[0]).all() and (IIR[1] == iir[1]).all())
from h5py import File
from os import listdir
import numpy as np
import scipy.signal as ss
dataPath = './Data/'
newPath = './Data.npz/'
h5Files = listdir(dataPath)
fs = 500
fl = 4
fh = 36
ext = .9
eps = 1e-5
N, Wn = ss.cheb2ord([fl*2/fs, fh*2/fs], [fl*ext*2/fs, fh/ext*2/fs], 3, 20)
b, a = ss.cheby2(N, 40, Wn, 'bandpass')
downSample = 5
fsamples = 9
W = 9
padded = fs+4
c = np.log(np.linspace(fl+1, fh, fh-fl)/np.linspace(fl, fh-1, fh-fl)) \
/np.log(fh/fl)*fsamples
w = np.zeros((fsamples, fh-fl))
w[0, 0] = c[0]
row = 0
for i in range(1, len(c)-1):
if np.sum(c[:i+1]) > row+1:
row += 1
w[row-1, i] = row-np.sum(c[:i])
w[row, i] = np.sum(c[:i+1])-row
else:
def get_filter(ftype='FIR',
band='lowpass',
order=None,
frequency=None,
sampling_rate=1000.,
**kwargs):
"""Compute digital (FIR or IIR) filter coefficients with the given
parameters.
Parameters
----------
ftype : str
Filter type:
* Finite Impulse Response filter ('FIR');
* Butterworth filter ('butter');
* Chebyshev filters ('cheby1', 'cheby2');
* Elliptic filter ('ellip');
* Bessel filter ('bessel').
band : str
Band type:
* Low-pass filter ('lowpass');
* High-pass filter ('highpass');
* Band-pass filter ('bandpass');
* Band-stop filter ('bandstop').
order : int
Order of the filter.
frequency : int, float, list, array
Cutoff frequencies; format depends on type of band:
* 'lowpass' or 'bandpass': single frequency;
* 'bandpass' or 'bandstop': pair of frequencies.
sampling_rate : int, float, optional
Sampling frequency (Hz).
``**kwargs`` : dict, optional
Additional keyword arguments are passed to the underlying
scipy.signal function.
Returns
-------
b : array
Numerator coefficients.
a : array
Denominator coefficients.
See Also:
scipy.signal
"""
# check inputs
if order is None:
raise TypeError("Please specify the filter order.")
if frequency is None:
raise TypeError("Please specify the cutoff frequency.")
if band not in ['lowpass', 'highpass', 'bandpass', 'bandstop']:
raise ValueError(
"Unknown filter type '%r'; choose 'lowpass', 'highpass', \
'bandpass', or 'bandstop'." % band)
# convert frequencies
frequency = _norm_freq(frequency, sampling_rate)
# get coeffs
b, a = [], []
if ftype == 'FIR':
# FIR filter
if order % 2 == 0:
order += 1
a = np.array([1])
if band in ['lowpass', 'bandstop']:
b = ss.firwin(numtaps=order,
cutoff=frequency,
pass_zero=True,
**kwargs)
elif band in ['highpass', 'bandpass']:
b = ss.firwin(numtaps=order,
cutoff=frequency,
pass_zero=False,
**kwargs)
elif ftype == 'butter':
# Butterworth filter
b, a = ss.butter(N=order,
Wn=frequency,
btype=band,
analog=False,
output='ba',
**kwargs)
elif ftype == 'cheby1':
# Chebyshev type I filter
b, a = ss.cheby1(N=order,
Wn=frequency,
btype=band,
analog=False,
output='ba',
**kwargs)
elif ftype == 'cheby2':
# chevyshev type II filter
b, a = ss.cheby2(N=order,
Wn=frequency,
btype=band,
analog=False,
output='ba',
**kwargs)
elif ftype == 'ellip':
# Elliptic filter
b, a = ss.ellip(N=order,
Wn=frequency,
btype=band,
analog=False,
output='ba',
**kwargs)
elif ftype == 'bessel':
# Bessel filter
b, a = ss.bessel(N=order,
Wn=frequency,
btype=band,
analog=False,
output='ba',
**kwargs)
return utils.ReturnTuple((b, a), ('b', 'a'))
def LPman(self, fil_dict):
self._get_params(fil_dict)
if not self._test_N():
return -1
self._save(fil_dict, sig.cheby2(self.N, self.A_SB, self.F_C,
btype='low', analog=self.analog, output=self.FRMT))
plt.ylim([-60, 12])
plt.ylabel('Amplitude [dB]')
plt.grid(which='both', axis='both')
plt.axvline(omega_c * np.pi, color='black') # cutoff frequency
plt.legend()
plt.savefig('ChebyshevT1.png')
# ---------- chebyshev 2 ----------
bArray = []
aArray = []
wArray = []
hArray = []
orderArray = [1, 2, 4, 5]
omega_c = 0.25
for i in orderArray:
b, a = signal.cheby2(N=i, rs=54, Wn=omega_c)
if i == 4:
filterSystems.append([b, a])
w, h = signal.freqz(b, a)
bArray.append(b)
aArray.append(a)
wArray.append(w)
hArray.append(h)
fig = plt.figure(figsize=(16, 9))
for index in range(len(orderArray)):
plt.plot(wArray[index],
20 * np.log10(abs(hArray[index])),
label="order = " + str(orderArray[index]))
plt.title('Chebyshev Type 2 Filter Frequency Response: Comparison')
plt.xlabel('Frequency [up to Nyquist]')
Ws = fs / fn # ローパスフィルタで波形整形 # バターワースフィルタ N, Wn = signal.buttord(Wp, Ws, gpass, gstop) b1, a1 = signal.butter(N, Wn, "low") y1 = signal.filtfilt(b1, a1, y) # 第一種チェビシェフフィルタ N, Wn = signal.cheb1ord(Wp, Ws, gpass, gstop) b2, a2 = signal.cheby1(N, gpass, Wn, "low") y2 = signal.filtfilt(b2, a2, y) # 第二種チェビシェフフィルタ N, Wn = signal.cheb2ord(Wp, Ws, gpass, gstop) b3, a3 = signal.cheby2(N, gstop, Wn, "low") y3 = signal.filtfilt(b3, a3, y) # 楕円フィルタ N, Wn = signal.ellipord(Wp, Ws, gpass, gstop) b4, a4 = signal.ellip(N, gpass, gstop, Wn, "low") y4 = signal.filtfilt(b4, a4, y) # ベッセルフィルタ N = 4 b5, a5 = signal.bessel(N, Ws, "low") y5 = signal.filtfilt(b5, a5, y) # FIR フィルタ a6 = 1 numtaps = n
"""
Created on Sat Apr 13 12:14:28 2019
@author: ivanpauno
"""
import scipy.signal as sig
import matplotlib.pyplot as plt
import filter_utils
# Comparación orden 3, att max 3dB
num, den = sig.butter(3, 1, analog=True) # n, wp
butter = sig.TransferFunction(num, den)
num, den = sig.cheby1(3, 3, 1, analog=True) # n, att max, wp
cheby1 = sig.TransferFunction(num, den)
num, den = sig.cheby2(3, 20, 1.539389818149637, analog=True) # n, att min, ws
cheby2 = sig.TransferFunction(num, den)
num, den = sig.bessel(3, 1, analog=True, norm='mag') # n, wp
bessel = sig.TransferFunction(num, den)
num, den = sig.ellip(3, 3, 20, 1, analog=True) # n, att max, att min, wp
ellip = sig.TransferFunction(num, den)
print('Transferencia Butterworth:\n')
filter_utils.pretty(butter.num, butter.den)
print('\n\n')
filter_utils.print_zpk(butter.num, butter.den)
print('\n\nTransferencia Chebyshev tipo 1:\n')
filter_utils.pretty(cheby1.num, cheby1.den)
print('\n\n')
filter_utils.print_zpk(cheby1.num, cheby1.den)
print('\n\nTransferencia Chebyshev tipo 2:\n')
def transform_signal(dat, s_freq, method, method_opt=None):
"""Transform the data using different methods.
Parameters
----------
dat : ndarray (dtype='float')
vector with all the data for one channel
s_freq : float
sampling frequency
method : str
one of 'cheby2', 'butter', 'morlet', 'morlet_real', 'hilbert', 'abs',
'moving_avg', 'gaussian'
method_opt : dict
depends on methods
Returns
-------
ndarray (dtype='float')
vector with all the data for one channel
Notes
-----
Wavelets pass only absolute values already, it does not make sense to store
the complex values.
Methods
-------
cheby2 has parameters:
freq : tuple of float
high and low values for bandpass
order : int
filter order
butter has parameters:
freq : tuple of float
high and low values for bandpass
order : int
filter order
morlet has parameters:
f0 : float
center frequency in Hz
sd : float
standard deviation of frequency
dur : float
window length in number of standard deviations
morlet_real has parameters:
freqs : ndarray
vector of wavelet frequencies for spindle detection
dur : float
duration of the wavelet (sec)
width : float
wavelet width
win : float
moving average window length (sec) of wavelet convolution
moving_avg has parameters:
dur : float
duration of the window (sec)
moving_rms has parameters:
dur : float
duration of the window (sec)
gaussian has parameters:
dur : float
standard deviation of the Gaussian kernel, aka sigma (sec)
"""
if 'cheby2' == method:
freq = method_opt['freq']
N = method_opt['order']
Rs = 80
nyquist = s_freq / 2
Wn = asarray(freq) / nyquist
b, a = cheby2(N, Rs, Wn, btype='bandpass')
dat = filtfilt(b, a, dat)
if 'butter' == method:
freq = method_opt['freq']
N = method_opt['order']
nyquist = s_freq / 2
Wn = asarray(freq) / nyquist
b, a = butter(N, Wn, btype='bandpass')
# print('butter: a=' + str(a) + ' b=' + str(b) + ' Wn=' + str(Wn) + ' N=' + str(N) + ' freq: ' + str(freq))
dat = filtfilt(b, a, dat)
if 'morlet' == method:
f0 = method_opt['f0']
sd = method_opt['sd']
dur = method_opt['dur']
wm = _wmorlet(f0, sd, s_freq, dur)
dat = absolute(fftconvolve(dat, wm, mode='same'))
if 'wavelet_real' == method:
freqs = method_opt['freqs']
dur = method_opt['dur']
width = method_opt['width']
win = int(method_opt['win'] * s_freq)
wm = _realwavelets(s_freq, freqs, dur, width)
tfr = empty((dat.shape[0], wm.shape[0]))
for i, one_wm in enumerate(wm):
x = abs(fftconvolve(dat, one_wm, mode='same'))
tfr[:, i] = fftconvolve(x, tukey(win), mode='same')
dat = mean(tfr, axis=1)
if 'hilbert' == method:
dat = hilbert(dat)
if 'abs' == method:
dat = absolute(dat)
if 'moving_avg' == method:
dur = method_opt['dur']
flat = ones(int(dur * s_freq))
dat = fftconvolve(dat, flat / sum(flat), mode='same')
if 'moving_rms' == method:
dur = method_opt['dur']
halfdur = int(floor(s_freq * dur / 2))
ldat = len(dat)
rms = zeros((ldat))
for i in range(ldat):
rms[i] = sqrt(
mean(square(dat[max(0, i - halfdur):min(ldat, i + halfdur)])))
dat = rms
if 'gaussian' == method:
sigma = method_opt['dur']
dat = gaussian_filter(dat, sigma)
return dat
print('Server Listening: {}'.format(server.server_address))
# reader in threading
reader_thread = threading.Thread(target=reader)
reader_thread.start()
# normal blocking server
shutdownEvent.wait(300)
q.join()
server.shutdown()
reader_thread.join()
# after stop show plot
ch1 = hampel(ch1_data, HAMPEL_WINDOW, 1)
ch2 = hampel(ch2_data, HAMPEL_WINDOW, 1)
#ch2 = kalman(ch2_data)
sos = cheby2(20, 40, 45, 'lowpass', fs=250, output='sos')
# sos1 = butter(20, 45, 'lowpass', fs=250, output='sos')
# ch2b = sosfilt(sos1, ch2)
ch1 = sosfilt(sos, ch1)
ch2 = sosfilt(sos, ch2)
'''
ch3 = []
aVR = []
aVL = []
aVF = []
for i in range(len(ch1)):
ch3.append(ch2[i] - ch1[i])
aVR.append(-0.5*(ch1[i]+ch2[i]))
aVL.append(ch1[i]-0.5*ch2[i])
aVF.append(ch2[i]-0.5*ch1[i])
def test_cheby2_5(self):
# Test case for bandpass filter without default
IIR = IIRDesign.cheby2(self.n, self.Rs, self.Ws2, ftype='bandpass')
iir = signal.cheby2(self.n, self.Rs, self.Ws2, btype='bandpass', fs=2)
self.assertTrue((IIR[0] == iir[0]).all() and (IIR[1] == iir[1]).all())
def __init__(self, _order, _cutoff, *args, **kwargs):
'''
Constructor to calculate the coefficients of the filter and set up various arrays/variables
to be used in the filter
Takes in:
_order = the order of the filter to by created
_cutoff = the cutoff frequency(s) of the filter normalised to sample rate
Optional:
filter_type = defines if the filter is lowpass/bandpass/highpass/bandstop
analogue_filter = defines the type of analogue filter to be replicated
cheby_ripple = defines the acceptable ripple in a chebyshev filter in dB
direct_form = defines if a direct form 1 or 2 filter is to be used
fixed_point = defines if a direct form 1 filter should be fixed point
'''
#Check the optional arguments
filter_type = kwargs.get('filter_type', 'low')
analogue_filter = kwargs.get('analogue_filter', 'butter')
cheby_ripple = kwargs.get('cheby_ripple', 5)
self.direct_form = kwargs.get('direct_form', 2)
self.fixed_point = kwargs.get('fixed_point', False)
#change the cutoffs to be normalised to Nyquist rather than sample rate
_cutoff = 2 * _cutoff
#select which type of analogue filter to replicate
#output = 'sos' to give second order sections coefficients
if analogue_filter == 'bessel':
self.sos = signal.bessel(_order,
_cutoff,
btype=filter_type,
analog=False,
output='sos')
elif analogue_filter == 'butter':
self.sos = signal.butter(_order,
_cutoff,
btype=filter_type,
analog=False,
output='sos')
elif analogue_filter == 'cheby1':
self.sos = signal.cheby1(_order,
cheby_ripple,
_cutoff,
btype=filter_type,
analog=False,
output='sos')
elif analogue_filter == 'cheby2':
self.sos = signal.cheby2(_order,
cheby_ripple,
_cutoff,
btype=filter_type,
analog=False,
output='sos')
#convert the coefficients to scaled integers if fixed point requested
#only available for Direct Form 1
self.fixed_scaling = 30
if self.fixed_point == True and self.direct_form == 1:
self.sos = self.sos * (2**self.fixed_scaling)
self.sos = self.sos.astype(int)
#define the number of second order sections required to implement that order of filter
shape = np.shape(self.sos)
self.sections = shape[0]
#set up arrays to store the x and y values for each second order section for direct form 1
self.x = np.zeros([(self.sections), 3])
self.y = np.zeros([(self.sections), 3])
#set up delays for direct form 2
self.delay = np.zeros([self.sections, 2])
def getI32(file_name, numberOfSlices, numberOfAllRepitionsParTable):
#fileSize = fileInfo.bytes/4
fid = open(file_name)
fileTable = np.fromfile(fid, dtype=np.float32)
#fpRawTime = fileTable[0:len(fileTable):4]
fpRawResp = fileTable[1:len(fileTable):4]
fpRawTrig = fileTable[2:len(fileTable):4]
fpRawCard = fileTable[3:len(fileTable):4]
# Process Respiration Data
# Merge 10 Values
N = 10
RespBLC = np.convolve(fpRawResp, np.ones((N, )) / N, mode='same')
# Evalute Baseline Shift
RespBLC = RespBLC - np.median(RespBLC, axis=None)
# derivative of respiration
kernel = [1, 0, -1]
RespDeriv = np.convolve(RespBLC, kernel, mode='same')
#RespDeriv = np.gradient(RespBLC)
# peak detection
pksRespMax, pksResMin = pk.peakdet(RespBLC * 20, delta=1)
print('avg. Respiration Rate: ' +
str(len(pksRespMax) / (len(RespBLC) / 60000)) + ' 1/min')
# Process Cardiac Data
fs = 1000 # Sampling Frequency(1 kHz)
lowcut = 2.5
highcut = 10.0
nyq = 0.5 * fs # Nyquist Frequency (Hz)
Wp = [lowcut / nyq,
highcut / nyq] # Passband Frequencies (Normalised 2.5 - 10 Hz)
Ws = [0.1 / nyq, 35 / nyq] # Stopband Frequencies (Normalised)
Rs = 40 # Sroppband Ripple (dB)
N = 3 # Filter order
b, a = sc.cheby2(N, Rs, Ws, btype='bandpass')
filtCardBLC = sc.filtfilt(b, a, fpRawCard)
N = 10
CardBLC = np.convolve(filtCardBLC, np.ones((N, )) / N, mode='same')
# Evalute Baseline Shift
CardBLC = CardBLC - np.median(CardBLC, axis=None)
# derivative of respiration
kernel = [1, 0, -1]
CardDeriv = np.convolve(CardBLC, kernel, mode='same')
# peak detection
pksCardpMax, pksCardMin = pk.peakdet(CardBLC * 20, delta=1)
print('avg. Card Rate: ' + str(len(pksCardpMax) / (len(CardBLC) / 60000)) +
' 1/min')
# if the trigger max is not equal 1 but higher
if max(fpRawTrig) != 1.0:
fpRawTrig = fpRawTrig - (max(fpRawTrig) - 1)
# find missing trigger and replace 1 by 0
idx_missedTrigger = np.where(np.diff(fpRawTrig, 2) == 2)[0] + 1
if len(idx_missedTrigger) > 0:
fpRawTrig[idx_missedTrigger + 1] = 0
triggerDataPoints = np.argwhere(fpRawTrig == 0)
numberOfTiggers = len(triggerDataPoints)
numberOfRepitions = numberOfTiggers / (numberOfSlices * 2)
print('Number of Repetitions: ' + str(numberOfRepitions))
# if two dataset in a single i32 file
if numberOfTiggers >= (
(numberOfAllRepitionsParTable + 5) * numberOfSlices * 2) * 2:
triggerDataPoints = triggerDataPoints[:int(
numberOfTiggers /
2)] # if more than two dataset in a single i32 file
old_numberOfTriggers = numberOfTiggers
# corrected number of triggers
numberOfTiggers = len(triggerDataPoints)
# if some wrong triggers in i32 file
if numberOfTiggers > (numberOfAllRepitionsParTable +
5) * numberOfSlices * 2:
wrongAmountOfTriggers = numberOfTiggers - (
numberOfAllRepitionsParTable + 5) * numberOfSlices * 2
fpRawTrig_cut = fpRawTrig[wrongAmountOfTriggers * 100 - 1::]
triggerDataPoints = np.argwhere(fpRawTrig_cut == 0)
numberOfTiggers = len(triggerDataPoints)
numberOfRepitions = numberOfTiggers / (numberOfSlices * 2)
print('Number of Repetitions: ' + str(numberOfRepitions))
triggerDataPoints_1st = triggerDataPoints[numberOfSlices * 5 *
2:numberOfTiggers:2, 0]
triggerDataPoints_2nd = triggerDataPoints[numberOfSlices * 5 * 2 +
1:numberOfTiggers:2, 0]
usedTriggerAmount = (
(numberOfAllRepitionsParTable + 5) * numberOfSlices * 2 -
5 * 2 * numberOfSlices) / 2
if not len(triggerDataPoints_1st) == len(triggerDataPoints_2nd):
print('Miss one Trigger in file_name in %s', file_name)
if len(triggerDataPoints_1st) < usedTriggerAmount:
if len(triggerDataPoints_2nd) == usedTriggerAmount:
triggerDataPoints_1st = triggerDataPoints_2nd
else:
sys.exit('Trigger does not relate to any slice or rep. Time')
if len(RespBLC) == len(CardBLC):
i32Table = np.zeros([len(RespBLC), 4])
else:
sys.exit('Respiration and Cardiac Data do not have the same length!')
i32Table[:, 0] = RespBLC
i32Table[:, 1] = RespDeriv
i32Table[:, 2] = CardBLC
i32Table[:, 3] = CardDeriv
return triggerDataPoints_1st, i32Table
def test_cheby2_3(self):
# Test case for highpass filter
IIR = IIRDesign.cheby2(self.n, self.Rs, self.Ws1, ftype='high')
iir = signal.cheby2(self.n, self.Rs, self.Ws1, btype='highpass', fs=2)
self.assertTrue((IIR[0] == iir[0]).all() and (IIR[1] == iir[1]).all())
from scipy import signal
import matplotlib.pyplot as plt
import numpy as np
b, a = signal.cheby2(4, 5, 100, 'low', analog=True)
w, h = signal.freqs(b, a)
plt.plot(w, 20 * np.log10(abs(h)))
plt.xscale('log')
plt.title('Chebyshev Type II frequency response (rp=5)')
plt.xlabel('Frequency [radians / second]')
plt.ylabel('Amplitude [dB]')
plt.margins(0, 0.1)
plt.grid(which='both', axis='both')
plt.axvline(100, color='green') # cutoff frequency
plt.axhline(-5, color='green') # rp
plt.show()
def HPman(self, fil_dict):
self.get_params(fil_dict)
self.save(fil_dict, sig.cheby2(self.N, self.A_SB, self.F_C,
btype='highpass', analog = self.analog, output = frmt))
def beam_profile_filter_chebyshev(self, filter_option):
'''
*This routine is filtering the beam profile with a type II Chebyshev
filter. The input is a library having the following structure and
informations:*
filter_option = {'type':'chebyshev', 'pass_frequency':pass_frequency, 'stop_frequency':stop_frequency, 'gain_pass':gain_pass, 'gain_stop':gain_stop}
*The function returns nCoefficients, the number of coefficients used
in the filter. You can also add the following option to plot and return
the filter transfer function:*
filter_option = {..., 'transfer_function_plot':True}
'''
noisyProfile = np.array(self.n_macroparticles)
freqSampling = 1 / (self.bin_centers[1] - self.bin_centers[0])
nyqFreq = freqSampling / 2.
frequencyPass = filter_option['pass_frequency'] / nyqFreq
frequencyStop = filter_option['stop_frequency'] / nyqFreq
gainPass = filter_option['gain_pass']
gainStop = filter_option['gain_stop']
# Compute the lowest order for a Chebyshev Type II digital filter
nCoefficients, wn = cheb2ord(frequencyPass, frequencyStop, gainPass,
gainStop)
# Compute the coefficients a Chebyshev Type II digital filter
b, a = cheby2(nCoefficients, gainStop, wn, btype='low')
# Apply the filter forward and backwards to cancel the group delay
self.n_macroparticles = filtfilt(b, a, noisyProfile)
self.n_macroparticles = np.ascontiguousarray(self.n_macroparticles)
if 'transfer_function_plot' in filter_option and filter_option[
'transfer_function_plot'] == True:
# Plot the filter transfer function
w, transferGain = freqz(b, a=a, worN=self.n_slices)
transferFreq = w / np.pi * nyqFreq
group_delay = -np.diff(-np.unwrap(-np.angle(transferGain))
) / -np.diff(w * freqSampling)
plt.figure()
ax1 = plt.subplot(311)
plt.plot(transferFreq, 20 * np.log10(abs(transferGain)))
plt.ylabel('Magnitude [dB]')
plt.subplot(312, sharex=ax1)
plt.plot(transferFreq, np.unwrap(-np.angle(transferGain)))
plt.ylabel('Phase [rad]')
plt.subplot(313, sharex=ax1)
plt.plot(transferFreq[:-1], group_delay)
plt.ylabel('Group delay [s]')
plt.xlabel('Frequency [Hz]')
## Plot the bunch spectrum and the filter transfer function
plt.figure()
plt.plot(
np.fft.fftfreq(self.n_slices,
self.bin_centers[1] - self.bin_centers[0]),
20. * np.log10(np.abs(np.fft.fft(noisyProfile))))
plt.xlabel('Frequency [Hz]')
plt.twinx()
plt.plot(transferFreq, 20 * np.log10(abs(transferGain)), 'r')
plt.xlim(0, plt.xlim()[1])
plt.show()
return nCoefficients, [transferFreq, transferGain]
else:
return nCoefficients, b, a
def BSman(self, fil_dict):
self.get_params(fil_dict)
self.save(fil_dict, sig.cheby2(self.N, self.A_SB, [self.F_C, self.F_C2],
btype='bandstop', analog = self.analog, output = frmt))
a_ft[imsize[0]//2-1, 0] = 1 # aliasing
a_ft[imsize[0]//2+1, 0] = 1 # aliasing
a_ft[imsize[0]-2, 0] = 1 # no aliasing
a_ft[2, 0] = 1 # no aliasing
a = np.fft.ifftn(a_ft)
if np.max(np.imag(a)) < 1e-5 * np.max(np.real(a)):
a = np.real(a)
else:
print('max imaginary part of a is ', np.max(np.imag(a)))
a_subsam1 = a[::subsam_factor,:]
#a_subsam2 = signal.decimate(a, 2, axis=0)
#num, den = signal.cheby1(4, 1, 0.2, 'low')
num, den = signal.cheby2(4, 25, 0.27, 'low')
#num, den = signal.butter(4, 0.16, 'low')
w, h = signal.freqz(num, den, imsize[0])
#w1, h1 = signal.freqz(num1, den1, imsize[0])
#a_filtered = signal.filtfilt(num, den, a, axis=0)
#a_subsam2 = a_filtered[::subsam_factor,:]
a_subsam2 = signal.decimate(a, subsam_factor, axis=0, ftype=signal.dlti(num, den))
#print(np.max(a_subsam2 - a_subsam3)) # 0.0
print(np.mean(a))
print(np.mean(a_subsam1))
print(np.mean(a_subsam2))
print()
print(np.max(a))
print(np.max(a_subsam1))
print(np.max(a_subsam2))
print()
def test_cheby2_1(self):
# Test case for lowpass filter with default
IIR = IIRDesign.cheby2(self.n, self.Rs, self.Ws1)
iir = signal.cheby2(self.n, self.Rs, self.Ws1, fs=2)
self.assertTrue((IIR[0] == iir[0]).all() and (IIR[1] == iir[1]).all())
def BSman(self, fil_dict):
self._get_params(fil_dict)
if not self._test_N():
return -1
self._save(fil_dict, sig.cheby2(self.N, self.A_SB, [self.F_C, self.F_C2],
btype='bandstop', analog=self.analog, output=self.FRMT))
def lowpass_cheby_2(data,
freq,
df,
maxorder=12,
ba=False,
freq_passband=False):
"""
Cheby2-Lowpass Filter
Filter data by passing data only below a certain frequency.
The main purpose of this cheby2 filter is downsampling.
This method will iteratively design a filter, whose pass
band frequency is determined dynamically, such that the
values above the stop band frequency are lower than -96dB.
Parameters
----------
data : array
Data to filter.
freq : float
The frequency above which signals are attenuated with 95 dB.
df : float
Sampling rate in Hz.
maxorder : int
Maximal order of the designed cheby2 filter.
**Default:** ``12``
ba : bool
If True return only the filter coefficients (b, a) instead of filtering.
**Default:** ``False``
freq_passband : bool
If True return additionally to the filtered data, the iteratively determined pass band frequency.
**Default:** ``False``
Returns
-------
data : array
Filtered data.
"""
nyquist = df * 0.5
# rp - maximum ripple of passband, rs - attenuation of stopband
rp, rs, order = 1, 96, 1e99
ws = freq / nyquist # stop band frequency
wp = ws # pass band frequency
# raise for some bad scenarios
if ws > 1:
ws = 1.0
msg = "Selected corner frequency is above Nyquist. " + \
"Setting Nyquist as high corner."
warnings.warn(msg)
while True:
if order <= maxorder:
break
wp = wp * 0.99
order, wn = cheb2ord(wp, ws, rp, rs, analog=0)
if ba:
return cheby2(order, rs, wn, btype='low', analog=0, output='ba')
z, p, k = cheby2(order, rs, wn, btype='low', analog=0, output='zpk')
sos = zpk2sos(z, p, k)
if freq_passband:
return sosfilt(sos, data), wp * nyquist
return sosfilt(sos, data)
def cheby2_bandpass(lowcut, highcut, fs, order=5):
nyq = 0.5 * fs
low = lowcut / nyq
high = highcut / nyq
b, a = cheby2(order, 60, [low, high], btype='bandpass')
return b, a
#from nnmnkwii.baseline.gmm import MLPG from nnmnkwii.paramgen import mlpg from Utils_GMM import GMM_M from KalmanSmoother import * from scipy.signal import butter, filtfilt from scipy import signal from nnmnkwii.util import trim_zeros_frames, remove_zeros_frames from keras.backend.tensorflow_backend import set_session config = tf.ConfigProto() config.gpu_options.allow_growth = True set_session(tf.Session(config=config)) # In[10]: fb, fa = signal.cheby2(10,40,7.0/(100/2),'low', analog=False)#, 'low', analog=True)#(4, 5, 100, 'low', analog=True) NoUnits=128#256 #LSTM units BatchSize=5 #50 NoEpoch=50 htkfile = HTK.HTKFile() std_frac=0.25 n_mfcc=13 inputDim=n_mfcc*3 OutDim=128 # In[11]: def Get_Wav_EMA_PerFile(EMA_file,Wav_file,F):
def start_CSP(self, signal_time, to_frequency = 128, baseline = True,\
base_time = 4, filt = 'ellip', method = 'pfu', train_tags = None):
"""Produces CSP filter from the data.
THIS VERSION CALCULATES ONE FILTER FOR ALL FREQUENCIES
The filter is stored in a variable P
Parameters:
-----------
signal_time : float
Time in seconds of signal to take as a class for maximalization
to_frequency [= 128Hz] : int
The frequency to which signal will be resampled
baseline [= True] : bool
If true a base line of base_time seconds will be taken as a class for minimalization
[If baseline = True]
base_time [= 4] : float
Time in seconds of baseline to take as minimalization class
filt [= 'ellip']: string ['ellip', 'cov', 'cheby', None]
a filter to use. If method is 'maxcontrast' the variable is set to None
method [= 'pfu'] : string ['pfu', 'regular','maxcontrast']
method of calculation CSP filter
train_tags : list
a list of tags to process. Each list entry is a tuple with first element position of tag in seconds, and second is a frequency of stimulation
"""
if not self.__is_int(to_frequency):
raise ValueError, 'to_frequency is not int!'
self.method = method
signal = self.parsed_data.prep_signal(
to_frequency,
self.electrodes,
montage=self.montage,
montage_channels=self.montage_channels)
if train_tags == None:
all_tags = self.parsed_data.get_train_tags(ccof=True)
else:
all_tags = train_tags
N = len(self.electrodes)
if method == 'maxcontrast' or method == 'minimalentropy':
baseline = True
filt = None
cov_pre = np.zeros([N, N])
cov_post = np.zeros([N, N])
pre_i = 0
post_i = 0
for i, frq in enumerate(self.frequencies):
if filt == 'ellip':
filt_b, filt_a = ellip(3, 0.1 , 100, \
[2*(frq - 1) / float(to_frequency), 2*(frq + 1) / float(to_frequency)],\
btype='pass')
signal_tmp = np.array(
[filtfilt(filt_b, filt_a, x) for x in signal])
elif filt == 'cheby':
filt_b, filt_a = cheby2(1, 10, [
2 * (frq - 1) / float(to_frequency), 2 *
(frq + 1) / float(to_frequency)
], 'pass')
signal_tmp = np.array(
[filtfilt(filt_b, filt_a, x) for x in signal])
elif filt == 'conv':
t_vec = np.linspace(0, 0.5 - 1.0 / to_frequency,
0.5 * to_frequency)
sin = np.sin(t_vec * 2 * np.pi)
sin /= sum(sin**2)
M = len(sin)
K = len(signal[0, :])
signal_tmp = np.array([
np.convolve(sin, x, mode='full')[M:K + M] for x in signal
])
elif filt == None:
signal_tmp = signal
tags = [x for (x, y) in all_tags if y == frq]
rest_tags = [x for (x, y) in all_tags if y != frq]
for idx in xrange(min(len(tags), len(rest_tags))):
s_post = signal_tmp[:, to_frequency * (tags[idx] ) : to_frequency * (tags[idx] +\
signal_time)]
dane_B = np.matrix(s_post)
R_B = dane_B * dane_B.T / np.trace(dane_B * dane_B.T)
cov_post += R_B
post_i += 1
if baseline:
if method == 'maxcontrast' or method == 'minimalentropy':
s_pre = signal_tmp[:, to_frequency *\
(tags[idx] + 1) : to_frequency * (tags[idx] + signal_time)]
dane_A = np.matrix(s_pre)
X = np.matrix(
self.__get_model_matrix(frq, s_pre.shape[1],
to_frequency))
Y = dane_A - (X.T * np.linalg.inv(X * X.T) * X *
dane_A.T).T
cov_pre += Y * Y.T / np.trace(Y * Y.T)
pre_i += 1
else:
s_pre = signal_tmp[:, to_frequency * (tags[idx] -\
1 - base_time) : to_frequency * (tags[idx] -1)]
dane_A = np.matrix(s_pre)
R_A = dane_A * dane_A.T / np.trace(dane_A * dane_A.T)
cov_pre += R_A
pre_i += 1
if not baseline:
for idx in rest_tags:
s_pre = signal_tmp[:, to_frequency * (idx ) : to_frequency *\
(idx + signal_time)]
dane_A = np.matrix(s_pre)
R_A = dane_A * dane_A.T / np.trace(dane_A * dane_A.T)
cov_pre += R_A
pre_i += 1
if method == 'regular' or method == 'maxcontrast':
self.P[:, :], self.vals = self.__get_filter(
cov_post / post_i, cov_pre / pre_i)
elif method == 'pfu':
self.P[:, :] = pfu_csp(cov_pre / pre_i, cov_post / post_i)
elif method == 'minimalentropy':
self.P[:, :], self.vals = self.__get_min_entropy(cov_pre / pre_i)
def test_cheby2_6(self):
# Test case for bandstop filter
IIR = IIRDesign.cheby2(self.n, self.Rs, self.Ws2, ftype='stop')
iir = signal.cheby2(self.n, self.Rs, self.Ws2, btype='bandstop', fs=2)
self.assertTrue((IIR[0] == iir[0]).all() and (IIR[1] == iir[1]).all())
'CB1': 60,
'O1': 61,
'Oz': 62,
'O2': 63,
'CB2': 64
}
# Only channel_idx is selected
channel_idx = [
channels[items]
for items in ['PZ', 'PO3', 'PO4', 'PO5', 'PO6', 'POz', 'O1', 'O2', 'Oz']
]
channel_idx = np.array(channel_idx) - 1
# bandpass filter
fmax = fs / 2
sos = cheby2(6, 20, [6 / fmax, 60 / fmax], btype='bandpass', output='sos')
# data path
dir_list = os.listdir(PathData)
dir_list.sort(
key=lambda a: int(re.findall('\d+', a)[0])) # sort list by numbers
for ii, f_name in enumerate(dir_list):
path1 = os.path.join(PathData, f_name)
temp_file = sio.loadmat(path1)
data = temp_file['data']
# select [0.5+0.14 s : 5.5+0.14 s] time window
time_index = np.arange((fs / 2) + round(subject_latency[ii] * fs),
t = str(data['FilterType'])
n = int(data['Order'])
fc1 = data['cutoff1']
fc2 = data['cutoff2']
att = int(data['attenuation'])
# Bandpass and Bandstop requires 2 cutoff points
if t == 'bandpass' or t == 'bandstop':
fc = [float(fc1), float(fc2)]
else:
fc = float(fc1)
# Generate filter coefficients
sos = signal.cheby2(N=n, rs=att, Wn=fc, btype=t, output='sos')
# Create empty dictionary with DirectForm field
out = {}
out['DirectForm'] = []
# Create as many fields of DirectForm as many the sos does in a json format
for i in range(len(sos)):
coeff = {
"i": i,
"b0": np.round(sos[i][0] * (2**14)),
"b1": np.round(sos[i][1] * (2**14)),
"b2": np.round(sos[i][2] * (2**14)),
def synthesizeQNTF(order=4, OSR=64, f0=0., NG=-60, ING=-20, n_im=None):
"""Synthesize a noise transfer function for a quadrature modulator.
**Parameters:**
order : int, optional
The order of the modulator. Defaults to 4.
OSR : int, optional
The oversampling ratio. Defaults to 64.
f0 : float, optional
The center frequency, normalized such that :math:`1 \\rightarrow f_s`.
Defaults to 0, ie to a low-pass modulator.
NG : float, optional
The in-band noise gain, expressed in dB. Defaults to -60.
ING : float, optional
The image-band noise gain, in dB. Defaults to -20.
n_im : int, optional
The number of in-band image zeros, defaults to ``floor(order/3)``.
**Returns:**
ntf : (z, p, k) tuple
``ntf`` is a zpk tuple containing the zeros, poles and the gain of the
synthesized NTF.
.. note::
From the MATLAB Delta-Sigma Toolbox:
ALPHA VERSION:
This function uses an experimental ad-hoc method that is
neither optimal nor robust.
**Example:**
Fourth order quadrature modulator::
from deltasigma import *
order = 4
osr = 32
NG = -50
ING = -10
f0 = 1 / 16
ntf0 = synthesizeQNTF(order, osr, f0, NG, ING)
pretty_lti(ntf0)
Returns::
(z - 0.888 - 0.4598j) (z - 0.9239 + 0.3827j) (z - 0.9239 - 0.3827j) (z - 0.953 - 0.3028j)
---------------------------------------------------------------------------------------------
(z - 0.5739 - 0.5699j) (z - 0.5913 - 0.2449j) (z - 0.6731 + 0.2788j) (z - 0.8088 - 0.0028j)
.. image:: _static/synthesizeQNTF.png
"""
if n_im is None:
n_im = np.floor(order/3)
debug_it = 0
if n_im == 0:
# Use synthesizeNTF to get an NTF with the specified NG; ignore ING
f1 = 0.5/OSR
x = 1.5
lowest_f = np.inf
dfdx = None
for itn in range(ITN_MAX):
ntf = synthesizeNTF(order, OSR, 1., x)
f = dbv(rmsGain(ntf, 0., f1)) - NG
if debug_it:
print('x=%.2f f=%.2f' % (x, f))
if abs(f) < 0.01:
break
if dfdx is None:
dx = 0.1*np.sign(f)
dfdx = 0
else:
dfdx = (f - f_old)/dx
dx_old = dx
dx = - f/dfdx
if abs(dx) > max((1, 2*abs(dx_old))):
dx = np.sign(dx)*max((1, 2*abs(dx_old)))
if x + dx <= 1:
# Hinf must be at least 1
dx = dx/2.
f_old = f
x = x + dx
if itn == ITN_MAX - 1:
warn('Iteration limit reached. NTF may be poor.')
# Rotate the NTF
z0 = np.exp(2j*np.pi*f0)
zeros, poles, k = _get_zpk(ntf)
ntf = (z0*zeros, z0*poles, k)
else:
n_in = order - n_im
f1 = f0 - 0.5/OSR
f2 = f0 + 0.5/OSR
z0 = np.exp(2j*np.pi*f0)
x = np.array([20., 20.])
# "R" parameters for cheby2()
lowest_f = np.inf
dfdx = np.array([float('NaN'), float('NaN')])
freq = np.linspace(-0.5, 0.5, 200)
for itn in range(ITN_MAX):
if debug_it:
print('\nx = [%.2f, %.2f]' % (x[0], x[1]))
b1, a1 = cheby2(n_in, x[0], 1./OSR, 'highpass')
b2, a2 = cheby2(n_im, x[1], 1./OSR, 'highpass')
ntf0 = (np.concatenate((np.roots(b1)*z0, np.roots(b2)*np.conj(z0))),
np.concatenate((np.roots(a1)*z0, np.roots(a2)*np.conj(z0))),
1)
m = evalTF(ntf0, np.exp(2j*np.pi*freq))
NG0 = dbv(rmsGain(ntf0, f1, f2))
ING0 = dbv(rmsGain(ntf0, -f1, -f2))
if debug_it:
import pylab as plt
from ._plotPZ import plotPZ
from ._figureMagic import figureMagic
plt.figure()
plt.subplot(121)
plotPZ(ntf0)
plt.subplot(122)
print('NG = %.1f, ING= %.1f' % (NG0, ING0))
plt.plot(freq, dbv(m))
figureMagic([-0.5, 0.5], 0.05, 2, [-100, 30], 10, 2)
plt.hold(True)
plt.plot([f1, f2], [NG0, NG0], 'k')
plt.text(np.mean([f1, f2]), NG0, ('NG=%.1fdB' % NG0), va='bottom')
plt.plot([-f1, -f2], [ING0, ING0], 'k')
plt.text(np.mean([-f1, -f2]), ING0, ('ING=%.1fdB' % ING0), va='bottom')
plt.show()
f = np.array([NG0 - NG, ING0 - ING])
if max(abs(f)) < 0.01:
break
if norm(f) < lowest_f:
lowest_f = norm(f)
# ntf0 is ALREADY a zpk tuple
zeros, poles, k = ntf0
best = (zeros.copy(), poles.copy(), k)
if abs(f[0]) > abs(f[1]):
# adjust x(1)
i = 0
else:
# adjust x(2)
i = 1
if np.isnan(dfdx[i]):
dx = np.sign(f[i])
dfdx[i] = 0
dfdx[1 - i] = float('NaN')
else:
dfdx[i] = (f[i] - f_old[i])/dx
dfdx[1 - i] = float('NaN')
dx = -f[i]/dfdx[i]
xnew = x[i] + dx
if xnew < 0.5*x[i]:
dx = -0.5*x[i]
else:
if xnew > 2*x[i]:
dx = x[i]
f_old = f.copy()
x[i] = x[i] + dx
if itn == ITN_MAX - 1:
warn('Iteration limit reached. NTF may be poor')
ntf = best
return ntf
# extract time = data[:, 0] * 1e-03 flow = data[:, 1] * 1e-03 N2 = data[:, 4] #-------------------- # SIGNAL PROCESSING #-------------------- # store raw time_raw = np.copy(time) flow_raw = np.copy(flow) # low-pass filter flow signal b, a = cheby2(4, 40, 0.05, btype='low') flow_f = filtfilt(b, a, flow) # re-sample time = np.arange(time[0], time[-1], dt) interpolant_flow = interp1d(time_raw, flow_f, kind='quadratic') flow_f = interpolant_flow(time) #flow_f = np.interp(time, time_raw, flow_f) interpolant_N2 = interp1d(time_raw, N2, kind='quadratic') N2 = interpolant_N2(time) #N2 = np.interp(time, time_raw, N2) # find start of washout st_estim = min(time[N2 < 0.5 * max(N2)]) - 0.5
def transform_signal(dat, s_freq, method, method_opt=None):
"""Transform the data using different methods.
Parameters
----------
dat : ndarray (dtype='float')
vector with all the data for one channel
s_freq : float
sampling frequency
method : str
one of 'cheby2', 'butter', 'morlet', 'morlet_real', 'hilbert', 'abs',
'moving_avg'
method_opt : dict
depends on methods
Returns
-------
ndarray (dtype='float')
vector with all the data for one channel
Notes
-----
Wavelets pass only absolute values already, it does not make sense to store
the complex values.
Methods
-------
cheby2 has parameters:
freq : tuple of float
high and low values for bandpass
order : int
filter order
butter has parameters:
freq : tuple of float
high and low values for bandpass
order : int
filter order
morlet has parameters:
f0 : float
center frequency in Hz
sd : float
standard deviation of frequency
dur : float
window length in number of standard deviations
morlet_real has parameters:
freqs : ndarray
vector of wavelet frequencies for spindle detection
dur : float
duration of the wavelet (sec)
width : float
wavelet width
win : float
moving average window length (sec) of wavelet convolution
moving_avg has parameters:
dur : float
duration of the window (sec)
"""
if 'cheby2' == method:
freq = method_opt['freq']
N = method_opt['order']
Rs = 80
nyquist = s_freq / 2
Wn = asarray(freq) / nyquist
b, a = cheby2(N, Rs, Wn, btype='bandpass')
dat = filtfilt(b, a, dat)
if 'butter' == method:
freq = method_opt['freq']
N = method_opt['order']
nyquist = s_freq / 2
Wn = asarray(freq) / nyquist
b, a = butter(N, Wn, btype='bandpass')
dat = filtfilt(b, a, dat)
if 'morlet' == method:
f0 = method_opt['f0']
sd = method_opt['sd']
dur = method_opt['dur']
wm = _wmorlet(f0, sd, s_freq, dur)
dat = absolute(fftconvolve(dat, wm, mode='same'))
if 'wavelet_real' == method:
freqs = method_opt['freqs']
dur = method_opt['dur']
width = method_opt['width']
win = method_opt['win'] * s_freq
wm = _realwavelets(s_freq, freqs, dur, width)
tfr = empty((dat.shape[0], wm.shape[0]))
for i, one_wm in enumerate(wm):
x = abs(fftconvolve(dat, one_wm, mode='same'))
tfr[:, i] = fftconvolve(x, tukeywin(win), mode='same')
dat = mean(tfr, axis=1)
if 'hilbert' == method:
dat = hilbert(dat)
if 'abs' == method:
dat = absolute(dat)
if 'moving_avg' == method:
dur = method_opt['dur']
flat = ones(int(dur * s_freq))
dat = fftconvolve(dat, flat / sum(flat), mode='same')
return dat
k=0
for x in df['path']:
k=k+1
spf = wave.open(x,'r')
signal = spf.readframes(-1)
signal = np.fromstring(signal, 'Int16')
frames=spf.getnframes()
max_amp,min_amp=get_min_max_amp(signal)
for i in range(0,frames):
signal[i]=(min_amp-signal[i]/max_amp-min_amp)*1000
beat=beat_cout(signal,0.25,max_amp)
# frinch_search_beat(signal,frames)
sos = sc.cheby2(10, 40, 17, btype='highpass', fs=4000, output='sos')
filtered = sc.sosfilt(sos, signal)
local_maxima_plot(signal)
# spectrum=fft.fft(signal)
# freq = fft.fftfreq(len(spectrum))
#
# threshold = 0.5 * max(abs(spectrum))
# mask = abs(spectrum) > threshold
# peaks = freq[mask]
# plot.plot(freq, abs(spectrum))
# plot.show()
# plot.plot(signal)
def monhe(raw, srate, show=0, show2=0, show3=1, filter=True):
"""
GREAT but:
discard crossings close to one another by less than 100 ms
"""
# 0 - Remove EMG, powerline and baseline shift
if filter:
rawend = prefilt(raw, srate, show)
else:
rawend = np.copy(raw)
# 0.5 - Choice sign of peaks (batch)
up = definepeak(rawend, srate)
# 1 - filter block (chebyshev 4th order 6-18 Hz)
nyqfreq = srate / 2.
filtband = [6 / nyqfreq, 18 / nyqfreq]
num, den = ss.cheby2(4, 40, filtband, btype='bandpass')
# filtafter2 = ss.filtfilt(num, den, raw)
filtafter = ss.filtfilt(num, den, rawend)
if show:
fig = pl.figure()
mngr = pl.get_current_fig_manager()
mngr.window.setGeometry(950, 50, 1000, 800)
ax = fig.add_subplot(411)
ax.plot(raw)
ax.set_title('raw signal')
ax = fig.add_subplot(412)
ax.plot(rawend)
ax.set_title('filtered from raw')
ax = fig.add_subplot(413)
# ax.plot(filtafter2)
ax.plot(filtafter, 'r')
ax.set_title('filtered for algorithm after preprocessing')
ax = fig.add_subplot(414)
ax.plot(filtafter)
ax.set_title('filtered for algorithm')
pl.show()
raw_input('cleaning')
# 2 - differentiate the signal and normalize according to max derivative in the signal
diffsig = np.diff(filtafter)
diffmax = np.max(np.abs(diffsig))
dsignal = diffsig / diffmax
# 3 - Get Shannon energy envelope
diffsquare = dsignal**2
logdiff = np.log(diffsquare)
shannon = -1 * diffsquare * logdiff
# 4 - Two sided zero-phase filtering
windowlen = 0.15 * srate # safe length of a QRS pulse
rectangular = ss.boxcar(windowlen)
smoothfirst = ss.convolve(shannon, rectangular, mode='same')
revfirst = smoothfirst[::-1]
smoothsec = ss.convolve(revfirst, rectangular, mode='same')
smoothfinal = smoothsec[::-1]
# 5 - Hilbert transform applied to the smoothed shannon energy envelope
hilbbuff = ss.hilbert(smoothfinal)
hilbsign = np.imag(hilbbuff)
# 6 - Get moving average of the hilbert transform so as to subtract after
n = int(2.5 * srate)
movwind = np.ones(n) / n
movav = ss.convolve(hilbsign, movwind, mode='same')
analyser = hilbsign - movav
# 7 - Get zero crossings (from negative to positive) of the 'analyser' signal
zero_crossings = np.where(np.diff(np.sign(analyser)))[0]
zero_crossings = zero_crossings[
zero_crossings >
0.05 * srate] # discard boundary effect that might appear at start
crossers = analyser[zero_crossings]
beats = zero_crossings[crossers < 0]
crossdiffs = np.diff(beats)
dangerous = crossdiffs < 0.15 * srate # to avoid stupid repetitions
dangerous = np.nonzero(dangerous)[0]
if len(dangerous):
print 'DANGER', beats[dangerous]
beats = np.delete(beats, dangerous)
# 7.1 -------- EXTRA ANTI-FALSE-POSITIVES --------
store_size = 5
index_store = 0
anti_fp = 0.26
anti_massive = 4
anti_badset = 3
reset_count = 0
cross_storer = np.zeros(store_size)
crossderivs = np.diff(analyser)
beats = sorted(list(beats))
iterator = beats[:]
evilbeats = []
for b in iterator:
cross_med = np.median(cross_storer)
# print 'info', b, crossderivs[b], anti_fp*cross_med, cross_med, anti_massive*cross_med
# massive slopes can be eliminated here too (decided not too because it helps in defining Agrafioti windows)
if crossderivs[b] > anti_fp * cross_med:
reset_count = 0
if crossderivs[b] < anti_massive * cross_med or cross_med < 1e-10:
# print 'store'
cross_storer[index_store] = crossderivs[b]
index_store += 1
if index_store == store_size:
index_store = 0
else:
reset_count += 1
print '\tEVIL SLOPE', b, crossderivs[
b], anti_fp * cross_med, reset_count
evilbeats.append(b)
beats.remove(b)
if reset_count >= anti_badset:
print '\tRESET'
reset_count = 0
cross_storer = np.zeros(store_size)
beats = np.array(beats, dtype=int)
evilbeats = np.array(evilbeats)
# 8 ----------------------------------------- Find the R-peak exactly -----------------------------------------
search = int(0.15 * srate)
adjacency = int(0.03 * srate)
diff_nr = int(0.01 * srate)
rawbeats = []
for b in xrange(len(beats)):
if beats[b] - search < 0:
rawwindow = rawend[0:beats[b] + search]
add = 0
elif beats[b] + search >= len(rawend):
rawwindow = rawend[beats[b] - search:len(rawend)]
add = beats[b] - search
else:
rawwindow = rawend[beats[b] - search:beats[b] + search]
add = beats[b] - search
# ----- get peaks -----
w_peaks = peakd.sgndiff(Signal=rawwindow)['Peak']
w_negpeaks = peakd.sgndiff(Signal=window, a=1)['Peak']
zerdiffs = np.where(np.diff(rawwindow) == 0)[0]
w_peaks = np.concatenate((w_peaks, zerdiffs))
w_negpeaks = np.concatenate((w_negpeaks, zerdiffs))
if up:
pospeaks = sorted(zip(rawwindow[w_peaks], w_peaks), reverse=True)
else:
pospeaks = sorted(zip(rawwindow[w_negpeaks], w_negpeaks))
# print '\n peaksssss', pospeaks
try:
twopeaks = [pospeaks[0]]
except IndexError:
twopeaks = []
# ----------- getting peaks -----------
for i in xrange(len(pospeaks) - 1):
if abs(pospeaks[0][1] - pospeaks[i + 1][1]) > adjacency:
twopeaks.append(pospeaks[i + 1])
break
poslen = len(twopeaks)
if poslen == 2:
# --- get maximum slope for max peak ---
if twopeaks[0][1] < diff_nr:
diff_f = np.diff(rawwindow[0:twopeaks[0][1] + diff_nr])
elif twopeaks[0][1] + diff_nr >= len(rawwindow):
diff_f = np.diff(rawwindow[twopeaks[0][1] -
diff_nr:len(rawwindow)])
else:
diff_f = np.diff(rawwindow[twopeaks[0][1] -
diff_nr:twopeaks[0][1] + diff_nr])
max_f = np.max(np.abs(diff_f))
# --- get maximum slope for second peak ---
if twopeaks[1][1] < diff_nr:
diff_s = np.diff(rawwindow[0:twopeaks[1][1] + diff_nr - 1])
elif twopeaks[1][1] + diff_nr >= len(rawwindow):
diff_s = np.diff(rawwindow[twopeaks[1][1] - diff_nr +
1:len(rawwindow)])
else:
diff_s = np.diff(rawwindow[twopeaks[1][1] - diff_nr +
1:twopeaks[1][1] + diff_nr - 1])
max_s = np.max(np.abs(diff_s))
if show2:
print 'diffs, main', diff_f, max_f, '\nsec', diff_s, max_s
if max_f > max_s:
# print '\tbigup'
assignup = [twopeaks[0][0], twopeaks[0][1]]
else:
# print '\tsmallup'
assignup = [twopeaks[1][0], twopeaks[1][1]]
rawbeats.append(assignup[1] + add)
elif poslen == 1:
rawbeats.append(twopeaks[0][1] + add)
else:
rawbeats.append(beats[b])
if show2:
fig = pl.figure()
mngr = pl.get_current_fig_manager()
mngr.window.setGeometry(950, 50, 1000, 800)
ax = fig.add_subplot(111)
ax.plot(rawwindow, 'b')
for i in xrange(poslen):
ax.plot(twopeaks[i][1], twopeaks[i][0], 'bo', markersize=10)
ax.plot(rawbeats[b] - add,
rawwindow[rawbeats[b] - add],
'yo',
markersize=7)
ax.grid('on')
ax.axis('tight')
pl.show()
raw_input('---')
pl.close()
# 8 ----------------------------------------- END OF POINT 8 -----------------------------------------
if show3:
fig = pl.figure()
mngr = pl.get_current_fig_manager()
mngr.window.setGeometry(950, 50, 1000, 800)
ax = fig.add_subplot(412)
ax.plot(rawend)
if len(rawbeats):
ax.plot(rawbeats, rawend[rawbeats], 'go')
ax.set_title('end signal')
ax = fig.add_subplot(411)
ax.plot(raw)
if beats.any():
ax.plot(beats, raw[beats], 'go')
ax.set_title('filtered from raw')
ax = fig.add_subplot(413)
ax.plot(smoothfinal)
ax.set_title('smooth shannon')
ax = fig.add_subplot(414)
ax.plot(analyser)
if beats.any():
ax.plot(beats, analyser[beats], 'go')
if evilbeats.any():
ax.plot(evilbeats, analyser[evilbeats], 'ro')
ax.plot(hilbsign, 'r')
ax.set_title('analysed signal')
pl.show()
raw_input('shannon')
# pl.close('all')
# kwrvals
kwrvals = {'Signal': rawend, 'R': sorted(list(frozenset(rawbeats)))}
return kwrvals
For digital filters, Wn are in the same units as fs. By default, fs is 2 half-cycles/sample, so these are normalized from 0 to 1, where 1 is the Nyquist frequency. (Wn is thus in half-cycles / sample.)
For analog filters, Wn is an angular frequency (e.g., rad/s).
"""
"""
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"""
sosTypeII = signal.cheby2(10, 20, fc, 'highpass', fs=2000, output='sos')
#cheby2 #rs = 20
#rs float The minimum attenuation required in the stop band. Specified in decibels, as a positive number.
filtered_II = signal.sosfilt(sosTypeII, s)
affichage('Exos 2 : After 25 Hz high-pass filter with Chebyshev Type II',2,s,filtered_II)
"""
███████ ██ ██ ██████ ███████ ██████
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def LPmin(self, fil_dict):
self.get_params(fil_dict)
self.N, self.F_SBC = cheb2ord(self.F_PB,self.F_SB, self.A_PB,self.A_SB,
analog = self.analog)
self.save(fil_dict, sig.cheby2(self.N, self.A_SB, self.F_SBC,
btype='lowpass', analog = self.analog, output = frmt))
def synthesizeQNTF(order=4, OSR=64, f0=0., NG=-60, ING=-20, n_im=None):
"""Synthesize a noise transfer function for a quadrature modulator.
**Parameters:**
order : int, optional
The order of the modulator. Defaults to 4.
OSR : int, optional
The oversampling ratio. Defaults to 64.
f0 : float, optional
The center frequency, normalized such that :math:`1 \\rightarrow f_s`.
Defaults to 0, ie to a low-pass modulator.
NG : float, optional
The in-band noise gain, expressed in dB. Defaults to -60.
ING : float, optional
The image-band noise gain, in dB. Defaults to -20.
n_im : int, optional
The number of in-band image zeros, defaults to ``floor(order/3)``.
**Returns:**
ntf : (z, p, k) tuple
``ntf`` is a zpk tuple containing the zeros, poles and the gain of the
synthesized NTF.
.. note::
From the MATLAB Delta-Sigma Toolbox:
ALPHA VERSION:
This function uses an experimental ad-hoc method that is
neither optimal nor robust.
**Example:**
Fourth order quadrature modulator::
from deltasigma import *
order = 4
osr = 32
NG = -50
ING = -10
f0 = 1 / 16
ntf0 = synthesizeQNTF(order, osr, f0, NG, ING)
pretty_lti(ntf0)
Returns::
(z - 0.888 - 0.4598j) (z - 0.9239 + 0.3827j) (z - 0.9239 - 0.3827j) (z - 0.953 - 0.3028j)
---------------------------------------------------------------------------------------------
(z - 0.5739 - 0.5699j) (z - 0.5913 - 0.2449j) (z - 0.6731 + 0.2788j) (z - 0.8088 - 0.0028j)
.. image:: _static/synthesizeQNTF.png
"""
if n_im is None:
n_im = np.floor(order/3)
debug_it = 0
if n_im == 0:
# Use synthesizeNTF to get an NTF with the specified NG; ignore ING
f1 = 0.5/OSR
x = 1.5
lowest_f = np.inf
dfdx = None
for itn in range(ITN_MAX):
ntf = synthesizeNTF(order, OSR, 1., x)
f = dbv(rmsGain(ntf, 0., f1)) - NG
#f_old = f
if debug_it:
print('x=%.2f f=%.2f' % (x, f))
if abs(f) < 0.01:
break
if dfdx is None:
dx = 0.1*np.sign(f)
dfdx = 0
else:
dfdx = (f - f_old)/dx
dx_old = dx
dx = - f/dfdx
if abs(dx) > max((1, 2*abs(dx_old))):
dx = np.sign(dx)*max((1, 2*abs(dx_old)))
if x + dx <= 1:
# Hinf must be at least 1
dx = dx/2.
f_old = f
x = x + dx
if itn == ITN_MAX - 1:
warn('Iteration limit reached. NTF may be poor.')
# Rotate the NTF
z0 = np.exp(2j*np.pi*f0)
zeros, poles, k = _get_zpk(ntf)
ntf = (z0*zeros, z0*poles, k)
else:
n_in = order - n_im
f1 = f0 - 0.5/OSR
f2 = f0 + 0.5/OSR
z0 = np.exp(2j*np.pi*f0)
x = np.array([20., 20.])
# "R" parameters for cheby2()
lowest_f = np.inf
dfdx = np.array([float('NaN'), float('NaN')])
freq = np.linspace(-0.5, 0.5, 200)
for itn in range(ITN_MAX):
if debug_it:
print('\nx = [%.2f, %.2f]' % (x[0], x[1]))
b1, a1 = cheby2(n_in, x[0], 1./OSR, 'highpass')
b2, a2 = cheby2(n_im, x[1], 1./OSR, 'highpass')
ntf0 = (np.concatenate((np.roots(b1)*z0, np.roots(b2)*np.conj(z0))),
np.concatenate((np.roots(a1)*z0, np.roots(a2)*np.conj(z0))),
1)
m = evalTF(ntf0, np.exp(2j*np.pi*freq))
NG0 = dbv(rmsGain(ntf0, f1, f2))
ING0 = dbv(rmsGain(ntf0, -f1, -f2))
if debug_it:
import pylab as plt
from ._plotPZ import plotPZ
from ._figureMagic import figureMagic
plt.figure()
plt.subplot(121)
plotPZ(ntf0)
plt.subplot(122)
print('NG = %.1f, ING= %.1f' % (NG0, ING0))
plt.plot(freq, dbv(m))
figureMagic([-0.5, 0.5], 0.05, 2, [-100, 30], 10, 2)
plt.hold(True)
plt.plot([f1, f2], [NG0, NG0], 'k')
plt.text(np.mean([f1, f2]), NG0, ('NG=%.1fdB' % NG0), va='bottom')
plt.plot([-f1, -f2], [ING0, ING0], 'k')
plt.text(np.mean([-f1, -f2]), ING0, ('ING=%.1fdB' % ING0), va='bottom')
plt.show()
f = np.array([NG0 - NG, ING0 - ING])
#f_old = f.copy()
if max(abs(f)) < 0.01:
break
if norm(f) < lowest_f:
lowest_f = norm(f)
# ntf0 is ALREADY a zpk tuple
zeros, poles, k = ntf0
best = (zeros.copy(), poles.copy(), k)
if abs(f[0]) > abs(f[1]):
# adjust x(1)
i = 0
else:
# adjust x(2)
i = 1
if np.isnan(dfdx[i]):
dx = np.sign(f[i])
dfdx[i] = 0
dfdx[1 - i] = float('NaN')
else:
dfdx[i] = (f[i] - f_old[i])/dx
dfdx[1 - i] = float('NaN')
dx = -f[i]/dfdx[i]
xnew = x[i] + dx
if xnew < 0.5*x[i]:
dx = -0.5*x[i]
else:
if xnew > 2*x[i]:
dx = x[i]
f_old = f.copy()
x[i] = x[i] + dx
if itn == ITN_MAX - 1:
warn('Iteration limit reached. NTF may be poor')
ntf = best
return ntf
def BSmin(self, fil_dict):
self.get_params(fil_dict)
self.N, self.F_SBC = cheb2ord([self.F_PB, self.F_PB2],
[self.F_SB, self.F_SB2], self.A_PB, self.A_SB, analog = self.analog)
self.save(fil_dict, sig.cheby2(self.N, self.A_SB, self.F_SBC,
btype='bandstop', analog = self.analog, output = frmt))
def get_filter(ftype='FIR',
band='lowpass',
order=None,
frequency=None,
sampling_rate=1000., **kwargs):
"""Compute digital (FIR or IIR) filter coefficients with the given
parameters.
Parameters
----------
ftype : str
Filter type:
* Finite Impulse Response filter ('FIR');
* Butterworth filter ('butter');
* Chebyshev filters ('cheby1', 'cheby2');
* Elliptic filter ('ellip');
* Bessel filter ('bessel').
band : str
Band type:
* Low-pass filter ('lowpass');
* High-pass filter ('highpass');
* Band-pass filter ('bandpass');
* Band-stop filter ('bandstop').
order : int
Order of the filter.
frequency : int, float, list, array
Cutoff frequencies; format depends on type of band:
* 'lowpass' or 'bandpass': single frequency;
* 'bandpass' or 'bandstop': pair of frequencies.
sampling_rate : int, float, optional
Sampling frequency (Hz).
``**kwargs`` : dict, optional
Additional keyword arguments are passed to the underlying
scipy.signal function.
Returns
-------
b : array
Numerator coefficients.
a : array
Denominator coefficients.
See Also:
scipy.signal
"""
# check inputs
if order is None:
raise TypeError("Please specify the filter order.")
if frequency is None:
raise TypeError("Please specify the cutoff frequency.")
if band not in ['lowpass', 'highpass', 'bandpass', 'bandstop']:
raise ValueError(
"Unknown filter type '%r'; choose 'lowpass', 'highpass', \
'bandpass', or 'bandstop'."
% band)
# convert frequencies
frequency = _norm_freq(frequency, sampling_rate)
# get coeffs
b, a = [], []
if ftype == 'FIR':
# FIR filter
if order % 2 == 0:
order += 1
a = np.array([1])
if band in ['lowpass', 'bandstop']:
b = ss.firwin(numtaps=order,
cutoff=frequency,
pass_zero=True, **kwargs)
elif band in ['highpass', 'bandpass']:
b = ss.firwin(numtaps=order,
cutoff=frequency,
pass_zero=False, **kwargs)
elif ftype == 'butter':
# Butterworth filter
b, a = ss.butter(N=order,
Wn=frequency,
btype=band,
analog=False,
output='ba', **kwargs)
elif ftype == 'cheby1':
# Chebyshev type I filter
b, a = ss.cheby1(N=order,
Wn=frequency,
btype=band,
analog=False,
output='ba', **kwargs)
elif ftype == 'cheby2':
# chevyshev type II filter
b, a = ss.cheby2(N=order,
Wn=frequency,
btype=band,
analog=False,
output='ba', **kwargs)
elif ftype == 'ellip':
# Elliptic filter
b, a = ss.ellip(N=order,
Wn=frequency,
btype=band,
analog=False,
output='ba', **kwargs)
elif ftype == 'bessel':
# Bessel filter
b, a = ss.bessel(N=order,
Wn=frequency,
btype=band,
analog=False,
output='ba', **kwargs)
return utils.ReturnTuple((b, a), ('b', 'a'))
def synthesizeChebyshevNTF(order=3, OSR=64, opt=0, H_inf=1.5, f0=0.):
"""Synthesize a noise transfer function for a delta-sigma modulator.
The NTF is a type-2 highpass Chebyshev function.
func:`synthesizeNTF` assumes that magnitude of the denominator of the NTF
is approximately constant in the passband. When the OSR or ``H_inf`` are
low, this assumption breaks down and synthesizeNTF yields a non-optimal
NTF. :func:`synthesizeChebyshevNTF` creates non-optimal NTFs, but fares
better than synthesizeNTF in the aforementioned circumstances.
**Parameters:**
order : int, optional
order of the modulator, defaults to 3
OSR : int, optional
oversampling ratio, defaults to 64
opt : int, optional
ignored value, for consistency with ::func:synthesizeNTF
H_inf : float, optional
maximum NTF gain, defaults to 1.5
f0 : float, optional
center frequency (1->fs), defaults to 0.
**Returns:**
z, p, k : tuple
a zpk tuple containing the zeros and poles of the NTF.
**Warns:**
* If a non-zero value is passed for ``opt``.
**Raises:**
* ValueError: Order must be even for a bandpass modulator
**Example:**
Compare the NTFs created by :func:`synthesizeNTF` and
:func:`synthesizeChebyshevNTF` when ``OSR`` is low::
OSR = 4
order = 8
H_inf = 3
H0 = synthesizeNTF(order,OSR,1,H_inf)
H1 = synthesizeChebyshevNTF(order,OSR,0,H_inf)
.. plot::
import pylab as plt
import numpy as np
from deltasigma import *
OSR = 4
order = 8
H_inf = 3
H0 = synthesizeNTF(order,OSR,1,H_inf)
H1 = synthesizeChebyshevNTF(order,OSR,0,H_inf)
# 1. Plot the singularities.
plotsize = (14, 7)
plt.subplot(121)
# we plot the singularities of the optimized NTF in light
# green with slightly bigger markers so that we can better
# distinguish the two NTF's when overlayed.
plotPZ(H1, markersize=7, color='#90EE90')
plt.hold(True)
plotPZ(H0, markersize=5)
plt.title('NTF Poles and Zeros')
f = np.concatenate((np.linspace(0, 0.75/OSR, 100), np.linspace(0.75/OSR, 0.5, 100)))
z = np.exp(2j*np.pi*f)
magH0 = dbv(evalTF(H0, z))
magH1 = dbv(evalTF(H1, z))
# 2. Plot the magnitude responses.
plt.subplot(222)
plt.plot(f, magH0, label='synthesizeNTF')
plt.hold(True)
plt.plot(f, magH1, label='synthesizeChebyshevNTF')
figureMagic([0, 0.5], 0.05, None, [-80, 20], 10, None, plotsize)
plt.xlabel('Normalized frequency ($1\\\\rightarrow f_s)$')
plt.ylabel('dB')
plt.legend(loc=4)
plt.title('NTF Magnitude Response')
# 3. Plot the magnitude responses in the signal band.
plt.subplot(224)
fstart = 0.01
f = np.linspace(fstart, 1.2, 200)/(2*OSR)
z = np.exp(2j*np.pi*f)
magH0 = dbv(evalTF(H0, z))
magH1 = dbv(evalTF(H1, z))
plt.semilogx(f*2*OSR, magH0, label='synthesizeNTF')
plt.hold(True)
plt.semilogx(f*2*OSR, magH1, label='synthesizeChebyshevNTF')
plt.axis([fstart, 1, -50, 0])
plt.grid(True)
sigma_H0 = dbv(rmsGain(H0, 0, 0.5/OSR))
sigma_H1 = dbv(rmsGain(H1, 0, 0.5/OSR))
plt.semilogx([fstart, 1], sigma_H0*np.array([1, 1]), linewidth=3, color='#191970')
plt.text(0.15, sigma_H0 + 1.5, 'RMS gain = %5.0fdB' % sigma_H0)
plt.semilogx([fstart, 1], sigma_H1*np.array([1, 1]), linewidth=3, color='#228B22')
plt.text(0.15, sigma_H1 + 1.5, 'RMS gain = %5.0fdB' % sigma_H1)
plt.xlabel('Normalized frequency ($1\\\\rightarrow f_B$)')
plt.ylabel('dB')
plt.legend(loc=3)
plt.tight_layout()
Repeat for ``H_inf`` low::
OSR = 32
order = 5
H_inf = 1.2
H0 = synthesizeNTF(order, OSR, 1, H_inf)
H1 = synthesizeChebyshevNTF(order, OSR, 1, H_inf)
.. plot::
import pylab as plt
import numpy as np
from deltasigma import *
OSR = 32
order = 5
H_inf = 1.2
H0 = synthesizeNTF(order, OSR, 1, H_inf)
H1 = synthesizeChebyshevNTF(order, OSR, 1, H_inf)
# 1. Plot the singularities.
plotsize = (14, 7)
plt.subplot(121)
# we plot the singularities of the optimized NTF in light
# green with slightly bigger markers so that we can better
# distinguish the two NTF's when overlayed.
plotPZ(H1, markersize=7, color='#90EE90')
plt.hold(True)
plotPZ(H0, markersize=5)
plt.title('NTF Poles and Zeros')
f = np.concatenate((np.linspace(0, 0.75/OSR, 100), np.linspace(0.75/OSR, 0.5, 100)))
z = np.exp(2j*np.pi*f)
magH0 = dbv(evalTF(H0, z))
magH1 = dbv(evalTF(H1, z))
# 2. Plot the magnitude responses.
plt.subplot(222)
plt.plot(f, magH0, label='synthesizeNTF')
plt.hold(True)
plt.plot(f, magH1, label='synthesizeChebyshevNTF')
figureMagic([0, 0.5], 0.05, None, [-80, 20], 10, None, plotsize)
plt.xlabel('Normalized frequency ($1\\\\rightarrow f_s)$')
plt.ylabel('dB')
plt.legend(loc=4)
plt.title('NTF Magnitude Response')
# 3. Plot the magnitude responses in the signal band.
plt.subplot(224)
fstart = 0.01
f = np.linspace(fstart, 1.2, 200)/(2*OSR)
z = np.exp(2j*np.pi*f)
magH0 = dbv(evalTF(H0, z))
magH1 = dbv(evalTF(H1, z))
plt.semilogx(f*2*OSR, magH0, label='synthesizeNTF')
plt.hold(True)
plt.semilogx(f*2*OSR, magH1, label='synthesizeChebyshevNTF')
plt.axis([fstart, 1, -60, -20])
plt.grid(True)
sigma_H0 = dbv(rmsGain(H0, 0, 0.5/OSR))
sigma_H1 = dbv(rmsGain(H1, 0, 0.5/OSR))
plt.semilogx([fstart, 1], sigma_H0*np.array([1, 1]), linewidth=3, color='#191970')
plt.text(0.15, sigma_H0 + 1.5, 'RMS gain = %5.0fdB' % sigma_H0)
plt.semilogx([fstart, 1], sigma_H1*np.array([1, 1]), linewidth=3, color='#228B22')
plt.text(0.15, sigma_H1 + 1.5, 'RMS gain = %5.0fdB' % sigma_H1)
plt.xlabel('Normalized frequency ($1\\\\rightarrow f_B$)')
plt.ylabel('dB')
plt.legend(loc=3)
plt.tight_layout()
"""
if opt:
warn("Got a non-zero 'opt' value. Not such optimization is " + \
"available, opt is only meant to ease switching between " + \
"synthesizeNTF and synthesizeChebyshevNTF.")
if f0 != 0:
if order % 2 != 0:
raise ValueError('Order must be even for a bandpass modulator.')
else:
f1, f2 = ds_f1f2(OSR, f0)
f1f2 = np.array([f1, f2])
x_min = 0
x_max = 300
dx_max = 10
ftol = 1e-06
xtol = 1e-06
x = 60
itn_limit = 10
converged = False
for itn in range(itn_limit):
if f0 == 0:
z, p, k = cheby2(order, x, 1./OSR, btype='high', output='zpk')
else:
z, p, k = cheby2(order/2., x, 2.*f1f2, btype='stop', output='zpk')
f = 1./k - H_inf
if f > 0:
x_max = x
else:
x_min = x
if itn == 0:
dx = -dx_max*np.sign(f)
else:
df = f - f_p
if abs(df) < ftol:
converged = True
break
dx = -f*dx/df
if converged:
break
x_p = x
f_p = f
x = max(x_min, min(x + dx, x_max))
dx = x - x_p
if abs(dx) < xtol:
break
ntf = (z, p, 1)
return ntf
def cheby_lowpass(wp, ws, fs, gpass, gstop):
wp = wp / fs
ws = ws / fs
order, wn = cheb2ord(wp, ws, gpass, gstop)
b, a = cheby2(order, gstop, wn)
return b, a
