def estimate(rg, filt, para, impulse, fs):
aa = zeros(len(rg))
Q = zeros(len(rg))
maxh = zeros(len(rg))
for i, freq in enumerate(rg):
filt[para] = freq
filt.compute(zeros(10000, dtype=float32))
w, h = freqz(filt.compute(impulse), worN=15000)
k1 = int(round(len(h) * 100.0 / fs))
k2 = int(round(len(h) * 10000.0 / fs))
B, A = invfreqz(w[k1 : k2 + 1], h[k1 : k2 + 1])
R = sqrt(A[2])
theta = math.acos(A[1] / (-2 * R))
aa[i] = fs * theta
frn = theta / (2 * pi)
Q[i] = (pi * frn) / (1 - R)
print "Pole frequency = %f Hz" % (aa[i] / (2 * pi))
# print 'Q = %f' % Q[i]
# print "R =", R
# print "frn =", frn, "theta =", theta
A = array((1, -2 * R * cos(theta), R * R))
w1, h1 = freqz(Bconst, A, worN=15000)
maxh[i] = max(abs(h))
# print "gain =", gain[i]
return aa, Q, maxh
def plot_response(self, ax):
# Plot the designed filter response
if self.n_section == 1:
fw, fh = signal.freqz(self.b, self.a, worN=self.Nfft)
ax.plot(fw, 20*log10(np.abs(fh)), linewidth=2, alpha=.75)
fxw, fxh = signal.freqz(self.fxb, self.fxa, worN=self.Nfft)
ax.plot(fxw, 20*log10(np.abs(fxh)), linestyle='--', linewidth=3,
alpha=.75)
# plot the simulated response, if simulated data exists
if self.xfavg is None or self.yfavg is None or self.pfavg is None:
pass
else:
# -- Fixed Point Sim --
xa = 2*pi * np.arange(self.Nfft)/self.Nfft
h = self.yfavg / self.xfavg
ax.plot(xa, 20*log10(h), linewidth=4, alpha=.5)
# -- Floating Point Sim --
hp = self.pfavg / self.xfavg
ax.plot(xa, 20*log10(hp), color='k', linestyle=':',
linewidth=2, alpha=.75)
ax.set_ylim(-80, 10)
ax.set_xlim(0, np.pi)
ax.set_ylabel('Magnitude dB');
ax.set_xlabel('Frequency Normalized Radians')
ax.legend(('Ideal', 'Quant. Coeff.',
'Fixed-P. Sim', 'Floating-P. Sim'))
def diffplot(freq, B, A, B2, A2):
w, h = sps.freqz(B, A)
w2, h2 = sps.freqz(B2, A2)
# h = h - h2
dabs = abs(h2) / abs(h)
dphase = np.unwrap(np.angle(h2)) - np.unwrap(np.angle(h))
fig = plt.figure()
plt.title('Difference between digital filter frequency responses')
ax1 = fig.add_subplot(111)
plt.plot(w * (freq/np.pi) / 2.0, 20 * np.log10(dabs), 'b')
plt.ylabel('Amplitude [dB]', color='b')
plt.xlabel('Frequency [rad/sample]')
ax2 = ax1.twinx()
angles = np.unwrap(np.angle(h))
angles = dphase
plt.plot(w * (freq/np.pi) / 2.0, angles, 'g')
plt.ylabel('Angle (radians)', color='g')
plt.grid()
plt.axis('tight')
plt.show()
def freqz(b, a=1, fs=1, xlim=None, N=1000, xlog=False):
"""Calculate the frequency response of a discrete time system over the
range xlim, over a log or linear interval.
Parameters
----------
b : array-like
Numerator coefficients of discrete time system
a : array-like, optional
Denominator coefficients of discrete time system
fs : float, optional
Sampling frequency; use to scale the output frequency array
xlim : tuple of (x_min, x_max), optional
Calculate the response from x_min to x_max. If omitted, the entire
digital frequency axis is used
N : int, optional
The number of points to calculate the system response at
xlog : bool, optional
Calculate the frequency response at a log (True) or linearly spaced
set of points"""
# Squeeze arrays to deal with cont2discrete array issues
b = np.squeeze(b)
a = np.squeeze(a)
if xlim is None:
w, resp = signal.freqz(b, a)
w = lin_or_logspace(w[w > 0][0], w[-1], N, True)
_, resp = signal.freqz(b, a, w)
else:
w = 2 * np.pi * lin_or_logspace(xlim[0], xlim[1], N, xlog) / fs
_, resp = signal.freqz(b, a, worN=w)
freq = w * fs / (2 * np.pi)
return freq, resp
def plot_filter(h, title, freq, gain, show=True):
if h.ndim == 2: # second-order sections
sos = h
n = mne.filter.estimate_ringing_samples(sos)
h = np.zeros(n)
h[0] = 1
h = signal.sosfilt(sos, h)
H = np.ones(512, np.complex128)
for section in sos:
f, this_H = signal.freqz(section[:3], section[3:])
H *= this_H
else:
f, H = signal.freqz(h)
fig, axs = plt.subplots(2)
t = np.arange(len(h)) / sfreq
axs[0].plot(t, h, color=blue)
axs[0].set(xlim=t[[0, -1]], xlabel='Time (sec)',
ylabel='Amplitude h(n)', title=title)
box_off(axs[0])
f *= sfreq / (2 * np.pi)
axs[1].semilogx(f, 10 * np.log10((H * H.conj()).real), color=blue,
linewidth=2, zorder=4)
plot_ideal(freq, gain, axs[1])
mne.viz.tight_layout()
if show:
plt.show()
def _find_min_max(self, f_start, f_stop, unit = 'dB'):
"""
Find minimum and maximum magnitude and the corresponding frequencies
for the filter defined in the filter dict in a given frequency band
[f_start, f_stop].
"""
w = np.linspace(f_start, f_stop, params['N_FFT'])*2*np.pi
[w, H] = sig.freqz(bb, aa, worN = w)
# add antiCausals if we have them
if (antiC):
#
# Evaluate transfer function of anticausal half on the same freq grid.
#
wa, ha = sig.freqz(bbA, aaA, worN = w)
ha = ha.conjugate()
#
# Total transfer function is the product
#
H = H*ha
f = w / (2.0 * pi) # frequency normalized to f_S
H_abs = abs(H)
H_max = max(H_abs)
H_min = min(H_abs)
F_max = f[np.argmax(H_abs)] # find the frequency where H_abs
F_min = f[np.argmin(H_abs)] # becomes max resp. min
if unit == 'dB':
H_max = 20*log10(H_max)
H_min = 20*log10(H_min)
return F_min, H_min, F_max, H_max
def compute_frequencies(self, N=None):
if hasattr(self, 'sample_rate'):
try:
self.W, self.H = signal.freqz(self.B, self.A)
except:
self.W, self.H = signal.freqz(self.B)
else:
self.W, self.H = signal.freqs(self.B, self.A, N)
def test_plot(self):
def plot(w, h):
assert_array_almost_equal(w, np.pi * np.arange(8.0) / 8)
assert_array_almost_equal(h, np.ones(8))
assert_raises(ZeroDivisionError,
freqz, [1.0], worN=8, plot=lambda w, h: 1 / 0)
freqz([1.0], worN=8, plot=plot)
def doplot2(B, A, B2, A2, freq = (315.0/88.0) * 8.0):
w, h = sps.freqz(B, A)
w2, h2 = sps.freqz(B2, A2)
# h.real /= C
# h2.real /= C2
begin = 0
end = len(w)
# end = int(len(w) * (12 / freq))
# chop = len(w) / 20
chop = 0
w = w[begin:end]
w2 = w2[begin:end]
h = h[begin:end]
h2 = h2[begin:end]
v = np.empty(len(w))
# print len(w)
hm = np.absolute(h)
hm2 = np.absolute(h2)
v0 = hm[0] / hm2[0]
for i in range(0, len(w)):
# print i, freq / 2 * (w[i] / pi), hm[i], hm2[i], hm[i] / hm2[i], (hm[i] / hm2[i]) / v0
v[i] = (hm[i] / hm2[i]) / v0
fig = plt.figure()
plt.title('Digital filter frequency response')
ax1 = fig.add_subplot(111)
v = 20 * np.log10(v )
# plt.plot(w * (freq/pi) / 2.0, v)
# plt.show()
# exit()
plt.plot(w * (freq/pi) / 2.0, 20 * np.log10(abs(h)), 'r')
plt.plot(w * (freq/pi) / 2.0, 20 * np.log10(abs(h2)), 'b')
plt.ylabel('Amplitude [dB]', color='b')
plt.xlabel('Frequency [rad/sample]')
ax2 = ax1.twinx()
angles = np.unwrap(np.angle(h))
angles2 = np.unwrap(np.angle(h2))
plt.plot(w * (freq/pi) / 2.0, angles, 'g')
plt.plot(w * (freq/pi) / 2.0, angles2, 'y')
plt.ylabel('Angle (radians)', color='g')
plt.grid()
plt.axis('tight')
plt.show()
def lab5_ex4():
# define coefficient arrays
b = firwin(20, 0.3) # given 10th degree polynomial
a = array([1.0]) # no feedback
# define quantized versions of 10th order array at Q3, Q6, Q8, Q16 (second array will always be 1.0)
q3 = fix(b * 2 ** 3) * 2 ** (
-3
) # (convert decimal into integer at N precision, then convert back into float decimal at same precision)
q6 = fix(b * 2 ** 6) * 2 ** (-6)
q8 = fix(b * 2 ** 8) * 2 ** (-8)
q16 = fix(b * 2 ** 16) * 2 ** (-16)
# define and plot full precision and quantized frequency responses on linear and dB scales
w, h = freqz(b, a)
subplot(211)
plot(w / pi, abs(h), "k-")
subplot(212)
plot(w / pi, 20 * log10(abs(h)), "k-")
w, h = freqz(q3, a)
subplot(211)
plot(w / pi, abs(h), "b-")
subplot(212)
plot(w / pi, 20 * log10(abs(h)), "b-")
w, h = freqz(q6, a)
subplot(211)
plot(w / pi, abs(h), "g-")
subplot(212)
plot(w / pi, 20 * log10(abs(h)), "g-")
w, h = freqz(q8, a)
subplot(211)
plot(w / pi, abs(h), "c-")
subplot(212)
plot(w / pi, 20 * log10(abs(h)), "c-")
w, h = freqz(q16, a)
subplot(211)
plot(w / pi, abs(h), "r-")
legend(("full precision", "Q3", "Q6", "Q8", "Q16"))
title("freq responses of 10th order filter by quantization and scale")
ylabel("linear scale")
subplot(212)
plot(w / pi, 20 * log10(abs(h)), "r-")
legend(("full precision", "Q3", "Q6", "Q8", "Q16"), loc=3)
ylabel("dB scale")
xlabel("normalized frequency")
show()
print (
"\nFilter's responses are quite different depending on the number of bits used for quantization. When using 3 bits especially, the filter's response is markedly different from it's response to the full precision signal. We can clearly see this effect on the dB scale, where it looks as if the number of bits available for quantization corresponds to the number of zeros/poles in the transfer function."
)
def butterfilt(data, sr, passband=(1.0, 50.0), stopband=(59., 61.),
order=(5, 5), plotfreqz=False, plotlim=100):
"""Wrapper for Butterworth filter of sample*channel*trial EEG data
Inputs:
data - sample*channel*trial EEG data
sr - sample rate (samps/sec)
Optional Inputs:
passband - low and high cutoffs for Butterworth passband
stopband - low and high cuttoffs for Butterworth stopband
Note that this should be used as a Notch filter
For countries w/ 60 Hz power lines (Americas etc.) use (59., 61.)
For countries w/ 50 Hz power lines (everywhere else) use (49., 51.)
order - Order of both Butterworth filters: (passband, stopband)
plotfreqz - Flag for plotting frequency responses of both filters
plotlim - Upper limit of frequencies to plot
Outputs:
filtdata - Filtered sample*channel*trial EEG data
"""
nyquist = .5 * float(sr)
b, a = butter(order[0], [float(passband[0]) / nyquist,
float(passband[1]) / nyquist], btype='bandpass')
filtdata = filtfilt(b, a, data, axis=0)
if plotfreqz:
w, h = freqz(b, a)
plt.plot((nyquist / np.pi) * w, abs(h))
plt.setp(plt.gca(),XLim=[0,plotlim],YLim=[0,1.1])
plt.plot([0, nyquist], [np.sqrt(0.5), np.sqrt(0.5)], '--')
plt.title(
'Butterworth Passband Frequency Response, Order = %d' % order[1])
if not not stopband:
B, A = butter(order[1], [float(stopband[0]) / nyquist,
float(stopband[1]) / nyquist],
btype='bandstop')
filtdata = filtfilt(B, A, data, axis=0)
if plotfreqz:
W, H = freqz(B, A)
plt.figure()
plt.plot((nyquist / np.pi) * W, abs(H))
plt.setp(plt.gca(),XLim=[0,plotlim],YLim=[0,1.1])
plt.plot([0, nyquist], [np.sqrt(0.5), np.sqrt(0.5)], '--')
plt.title(
'Butterworth Stopband Frequency Response, Order = %d'
% order[1])
return filtdata
def output_freqz_libcrybaby():
from pluginloader import Plugin
filt = Plugin("../build/default/src/plugins/libcrybaby.so")
filt['crybaby2.refvolt'] = 0.1
para = 'crybaby2.hotpotz'
name = filt.get_var_attr(para)[0]
fs = 44100
filt.init(fs)
impulse = zeros(10000,dtype=float32)
impulse[0] = 1
rg = log10(linspace(*np.power(10,filt.get_range(para)), num=20))
if False:
aa, Q, maxh, p1, Bconst, freq_const = estimate(rg, filt, para, impulse, fs)
pickle.dump((aa,Q,maxh,p1,Bconst,freq_const), file("p.out","w"))
else:
aa, Q, maxh, p1, Bconst, freq_const = pickle.load(file("p.out"))
z1, z2A, z3A, gcA = estimate_SR(filt, para, freq_const, impulse)
off, a1A, qA = fit_param(rg, aa, Q, fs)
gain, g_off, gA = make_gain(rg, off, a1A, qA, maxh, p1, Bconst, fs)
#show_param(rg, off, g_off, aa, a1A, Q, qA, gain, gA)
rg = log10(linspace(*np.power(10,filt.get_range(para)), num=10))
filt.init(fs)
for i, freq in enumerate(rg):
filt[para] = freq
filt.compute(zeros(10000,dtype=float32))
w, h = freqz(filt.compute(impulse), worN=15000)
q = polyval(qA, freq)
a1 = (off - 1 / polyval(a1A, freq)) / fs
g = g_off - 1 / polyval(gA, freq)
gc = polyval(gcA, fs)
r = 1 - a1/(2*q)
A = array((1, -2*r*cos(a1), r*r))
A = poly(list(roots(A))+[p1])
B = poly([polyval(z2A,fs),polyval(z3A,fs),z1])
w1, h1 = freqz(B*g*gc, A, worN=15000)
semilogx((w*fs/(2*pi))[1:], 20*log10(abs(h[1:])), "b")
semilogx((w1*fs/(2*pi))[1:], 20*log10(abs(h1[1:])), "r")
print "theta2pi = (%g - 1000 / (%s)) / SR;" % (off, string_polyval(a1A*1000, "wah"))
print "Q = %s;" % string_polyval(qA, "wah")
print "g = %g - 1 / (%s);" % (g_off, string_polyval(gA, "wah"))
print "gc = %s;" % string_polyval(gcA, "SR")
print "p1 = exp(-1000/(%g*SR));" % (-1000/(fs*log(p1)))
print "z1 = %g;" % z1
print "z2 = %s;" % string_polyval(z2A, "SR")
print "z3 = %s;" % string_polyval(z3A, "SR")
show()
def fourier(self,List=None,fs=1):
if type(List) is list:
indices=self.getInds(List=List)
if 0 not in indices:
List.append((0,0))
domain=[int(self.getDom(List=List)[0]),int(self.getDom(List=List)[1])]
for i in range(domain[0],domain[1]+1,1):
if i not in indices:
List.append((i,0))
indices=self.getInds(List=List)
values=self.getVals(List=List)
f_indices,f_values=freqz(values,indices,worN=2000)
f_indices=f_indices*(fs * 0.5 / np.pi)
f_List=[]
f_indices=list(f_indices)
values_copy=f_values.copy()
values_copy=list(values_copy)
f_values=list(f_values)
i=0
for value in f_values:
f_List.append((f_indices[i],float(np.real(f_values[i]))))
i=i+1
return f_List
else:
List=self.points
indices=self.getInds(List=List)
if 0 not in indices:
List.append((0,0))
domain=[int(self.getDom(List=List)[0]),int(self.getDom(List=List)[1])]
for i in range(domain[0],domain[1]+1,1):
if i not in indices:
List.append((i,0))
indices=self.getInds(List=List)
values=self.getVals(List=List)
f_indices,f_values=freqz(values,indices,worN=2000)
f_indices=f_indices*(fs * 0.5 / np.pi)
f_List=[]
f_indices=list(f_indices)
values_copy=f_values.copy()
values_copy=list(values_copy)
f_values=list(f_values)
i=0
for value in f_values:
f_List.append((f_indices[i],float(np.real(f_values[i]))))
i=i+1
return f_List
def iir_bandstops(fstops, fs, order=4):
"""ellip notch filter
fstops is a list of entries of the form [frequency (Hz), df, df2]
where df is the pass width and df2 is the stop width (narrower
than the pass width). Use caution if passing more than one freq at a time,
because the filter response might behave in ways you don't expect.
"""
nyq = 0.5 * fs
# Zeros zd, poles pd, and gain kd for the digital filter
zd = np.array([])
pd = np.array([])
kd = 1
# Notches
for fstopData in fstops:
fstop = fstopData[0]
df = fstopData[1]
df2 = fstopData[2]
low = (fstop - df) / nyq
high = (fstop + df) / nyq
low2 = (fstop - df2) / nyq
high2 = (fstop + df2) / nyq
z, p, k = iirdesign([low,high], [low2,high2], gpass=1, gstop=6,
ftype='ellip', output='zpk')
zd = np.append(zd,z)
pd = np.append(pd,p)
# Set gain to one at 100 Hz...better not notch there
bPrelim,aPrelim = zpk2tf(zd, pd, 1)
outFreq, outg0 = freqz(bPrelim, aPrelim, 100/nyq)
# Return the numerator and denominator of the digital filter
b,a = zpk2tf(zd,pd,k)
return b, a
def frequency_response(self, n=10000):
"""
Generate a filter frequency response from a set of filter taps.
Returns plottable (x, y) with respect to an actual sampling rate
"""
w, h = signal.freqz(self.b, self.a, worN=n)
return (0.5 * self.fs * w / np.pi, np.abs(h))
def plot_filter_characteristics(self):
w, h = freqz(self.freq_filter.num, self.freq_filter.denom)
plt.figure(1)
plt.subplot(2,1,1)
plt.hold(True)
powa = plt.plot((self.filter_parameters.sample_rate*0.5/pi)*w, abs(h),'b-', label = 'Char. amplitudowa')
plt.title('Charakterystyki filtru')
plt.xlabel('Czestotliwosc [Hz]')
plt.ylabel('Amplituda')
plt.twinx(ax=None)
angles = unwrap(angle(h))
plt.znie = plot((self.filter_parameters.sample_rate*0.5/pi)*w,angles, 'g-', label = 'Char. fazowa')
plt.ylabel('Faza')
plt.grid()
tekst = powa + znie
wybierz = [l.get_label() for l in tekst]
plt.legend(tekst, wybierz, loc='best')
########################################################################################################################
plt.subplot(2,1,2)
w2, gd = group_delay((num, denom))
plt.plot((sample_rate*0.5/pi)*w2, gd)
plt.grid()
plt.xlabel('Czestotliwosc [Hz]')
plt.ylabel('Opoznienie grupowe [probki]')
plt.title('Opoznienie grupowe filtru')
plt.show()
def __init__(self, fir_len, fir_bits, tb_width):
tb_ctr = 1/(2*4)
pass_corner = tb_ctr - (tb_ctr*tb_width/2)
stop_corner = tb_ctr + (tb_ctr*tb_width/2)
fir_bands = [0, pass_corner, stop_corner, 0.5]
b = signal.remez(fir_len, fir_bands, [1, 0])
coeff_scl = 2**(fir_bits-1)
self.fir_coeff = np.floor(b*coeff_scl + 0.5)
# Dump Coefficients?
if 1:
write_meminit("fir4dec_coeff.v", self.fir_coeff)
self.fir_coeff = self.fir_coeff/coeff_scl;
# plot FIR response?
if 1:
W, H = signal.freqz(self.fir_coeff)
plt.figure()
plt.plot(W/(2*np.pi), 20*np.log10(np.abs(H)))
plt.grid()
plt.xlabel("Freq (normalized)")
plt.ylabel("dB")
plt.title("fir4dec response (close to continue sim)")
plt.show()
def filter_VE(data):
f=np.linspace(0,1,50000)
a = np.ones(50000)
#Switching power supply frequency (~290 KHz)
a[2850:2950] =0
#1.49 MHz
a[14850:14950]=0
#AM 1.37 MHz
a[13650:13750] = 0
#80 m Ham band (3.97 MHz)
a[39650:39750] = 0
#80 m Ham band (4 MHz)
a[39950:40050]= 0
a[-1]=0
b=sigs.firwin2(3000,f,a)
[h, fpoints] = sigs.freqz(b, 1, 50000,10E6)
#Run the FIR filter
vec = sigs.lfilter(b,1,data)
return vec
def main():
edges = [30, 60, 120, 240]
corners = zip(edges[:-1], edges[1:])
centres = [(a + b) / 2 for a, b in corners]
#c = [get_linkwitz_riley_coeffs(1, b, a, edges[-1] * 2) for b, a in corners]
sr = 2000
c = [get_peak_coeffs(-24, i, sr, 1) for i in centres]
c.append([[1, 0, 0], [1, 0, 0]])
bm = [BiquadMemory(0, 0) for _ in c]
bc = [BiquadCoefficients(b0, b1, b2, a1, a2)
for [b0, b1, b2], [a0, a1, a2] in c]
c.append(series_coeffs(c))
# c.append(impedance_filter(c[-1]))
wh = [signal.freqz(b, a) for b, a in c]
plt.subplot(111)
plt.title("Frequency response - reflection filter")
for w, h in wh:
plt.semilogx(w, 20 * np.log10(np.abs(h)))
plt.ylabel('Amplitude Response (dB)')
plt.xlabel('Frequency (rad/sample)')
plt.grid()
plt.show()
def test_hilbert(self):
N = 11 # number of taps in the filter
a = 0.1 # width of the transition band
# design an unity gain hilbert bandpass filter from w to 0.5-w
h = remez(11, [a, 0.5-a], [1], type='hilbert')
# make sure the filter has correct # of taps
assert_(len(h) == N, "Number of Taps")
# make sure it is type III (anti-symmetric tap coefficients)
assert_array_almost_equal(h[:(N-1)//2], -h[:-(N-1)//2-1:-1])
# Since the requested response is symmetric, all even coeffcients
# should be zero (or in this case really small)
assert_((abs(h[1::2]) < 1e-15).all(), "Even Coefficients Equal Zero")
# now check the frequency response
w, H = freqz(h, 1)
f = w/2/np.pi
Hmag = abs(H)
# should have a zero at 0 and pi (in this case close to zero)
assert_((Hmag[[0, -1]] < 0.02).all(), "Zero at zero and pi")
# check that the pass band is close to unity
idx = np.logical_and(f > a, f < 0.5-a)
assert_((abs(Hmag[idx] - 1) < 0.015).all(), "Pass Band Close To Unity")
def test_firls(self):
N = 11 # number of taps in the filter
a = 0.1 # width of the transition band
# design a halfband symmetric low-pass filter
h = firls(11, [0, a, 0.5-a, 0.5], [1, 1, 0, 0], fs=1.0)
# make sure the filter has correct # of taps
assert_equal(len(h), N)
# make sure it is symmetric
midx = (N-1) // 2
assert_array_almost_equal(h[:midx], h[:-midx-1:-1])
# make sure the center tap is 0.5
assert_almost_equal(h[midx], 0.5)
# For halfband symmetric, odd coefficients (except the center)
# should be zero (really small)
hodd = np.hstack((h[1:midx:2], h[-midx+1::2]))
assert_array_almost_equal(hodd, 0)
# now check the frequency response
w, H = freqz(h, 1)
f = w/2/np.pi
Hmag = np.abs(H)
# check that the pass band is close to unity
idx = np.logical_and(f > 0, f < a)
assert_array_almost_equal(Hmag[idx], 1, decimal=3)
# check that the stop band is close to zero
idx = np.logical_and(f > 0.5-a, f < 0.5)
assert_array_almost_equal(Hmag[idx], 0, decimal=3)
def freq_response(b, a=1., n_freqs=1024, sides='onesided'):
"""
Returns the frequency response of the IIR or FIR filter described
by beta and alpha coefficients.
Parameters
----------
b : beta sequence (moving average component)
a : alpha sequence (autoregressive component)
n_freqs : size of frequency grid
sides : {'onesided', 'twosided'}
compute frequencies between [-PI,PI), or from [0, PI]
Returns
-------
fgrid, H(e^jw)
Notes
-----
For a description of the linear constant-coefficient difference equation,
see
http://en.wikipedia.org/wiki/Z-transform
"""
# transitioning to scipy freqz
real_n = n_freqs // 2 + 1 if sides == 'onesided' else n_freqs
return sig.freqz(b, a=a, worN=real_n, whole=sides != 'onesided')
def highpass(signal, Fs, fc=constants.fc_hp, plot=False):
'''
Filter out the really low frequencies, default is below 50Hz
'''
# have some predefined parameters
rp = 5 # minimum ripple in dB in pass-band
rs = 60 # minimum attenuation in dB in stop-band
n = 4 # order of the filter
type = 'butter'
# normalized cut-off frequency
wc = 2. * fc / Fs
# design the filter
from scipy.signal import iirfilter, lfilter, freqz
b, a = iirfilter(n, Wn=wc, rp=rp, rs=rs, btype='highpass', ftype=type)
# plot frequency response of filter if requested
if (plot):
import matplotlib.pyplot as plt
w, h = freqz(b, a)
plt.figure()
plt.title('Digital filter frequency response')
plt.plot(w, 20 * np.log10(np.abs(h)))
plt.title('Digital filter frequency response')
plt.ylabel('Amplitude Response [dB]')
plt.xlabel('Frequency (rad/sample)')
plt.grid()
# apply the filter
signal = lfilter(b, a, signal.copy())
return signal
def _filter_resp(b, a, sampling_rate=1000., nfreqs=512):
"""Compute the filter frequency response.
Parameters
----------
b : array
Numerator coefficients.
a : array
Denominator coefficients.
sampling_rate : int, float, optional
Sampling frequency (Hz).
nfreqs : int, optional
Number of frequency points to compute.
Returns
-------
freqs : array
Array of frequencies (Hz) at which the response was computed.
resp : array
Frequency response.
"""
w, resp = ss.freqz(b, a, nfreqs)
# convert frequencies
freqs = w * sampling_rate / (2. * np.pi)
return freqs, resp
def plot_response(self, filename=None):
"""
Plot frequency response.
.. note:: The follow phase response is obtained in case :meth:`lfilter` is used. The method :meth:`filtfilt` results in a zero-phase response.
"""
fs = self.sample_frequency
fig = plt.figure()
ax1 = fig.add_subplot(211)
ax2 = fig.add_subplot(212)
for f, fc in zip(self.filters, self.frequencies.center):
w, h = freqz(f[0], f[1], int(fs/2))#np.arange(fs/2.0))
ax1.semilogx(w / (2.0*np.pi) * fs, 20.0 * np.log10(np.abs(h)), label=str(int(fc)))
ax2.semilogx(w / (2.0*np.pi) * fs, np.angle(h), label=str(int(fc)))
ax1.set_xlabel(r'$f$ in Hz')
ax1.set_ylabel(r'$|H|$ in dB re. 1')
ax2.set_xlabel(r'$f$ in Hz')
ax2.set_ylabel(r'$\angle H$ in rad')
ax1.legend(loc=5)
ax2.legend(loc=5)
ax1.set_ylim(-60.0, +10.0)
if filename:
fig.savefig(filename)
else:
return fig
def lock(self, f0=None, bw_ratio=0.5, coeff_ratio=9., bw=None, coeffs=None,
window='blackman'):
"""Standard, windowed finite impulse response filter. """
t = self.t
fs = self.fs
if f0 is None:
self.f0 = f0 = self.f0_est
else:
self.f0 = f0
if bw is None:
bw = bw_ratio * f0 / (self.fs/2)
else:
bw = bw / (self.fs/2)
if coeffs is None:
coeffs = round(coeff_ratio / bw, 0)
if coeffs > self.x.size:
raise ValueError(
"""No valid output when 'coeffs' > t.size (coeffs: {}, t.size: {}).
Reduce coeffs by increasing bw, bw_ratio, or decreasing coeff_ratio,
or provide more data.""".format(coeffs, t.size))
self.fir = b = signal.firwin(coeffs, bw, window=window)
w, rep = signal.freqz(b, worN=np.pi*np.array([0., bw/2, bw, f0/self.fs, f0/(self.fs/2.), 1.]))
print("Response:")
_print_magnitude_data(w, rep, fs)
self.run(f0=f0)
def lock_butter(self, N, f3dB, t_exclude=0, f0=None, print_response=True):
t = self.t
fs = self.fs
nyq = fs / 2.
f3dB = f3dB / nyq
self.iir = ba = signal.iirfilter(N, f3dB, btype='low')
if f0 is None:
self.f0 = f0 = self.f0_est
self.z = z = signal.lfilter(self.iir[0], self.iir[1], self.z)
# TODO: Fix accounting on final / initial point
m = self.m
self.m = self.m & (t >= (t[m][0] + t_exclude)) & (t < (t[m][-1] - t_exclude))
self.A = abs(self.z)
self.phi = np.angle(self.z)
if print_response:
w, rep = signal.freqz(self.iir[0], self.iir[1],
worN=np.pi*np.array([0., f3dB/2, f3dB,
0.5*f0/nyq, f0/nyq, 1.]))
print("Response:")
_print_magnitude_data(w, rep, fs)
def lab3_ex4():
# assign pre-defined (arbitrary) variables
To = 125.0*(10**-6) #signal period = 125 microseconds
L = 1*(10**-6) #inductance = 1 microHenry
C = 4*(10**-6) #capacitance = 4 microFarads
# calculate oscillator frequency
Fo = 1/To
print("\nAssuming signal period is is 125 microseconds, oscillator frequency is 1/T:\n" + str(Fo) + " Hz")
# calculate sampling frequency (should be at least 2x, but using 10x here since best practice) and sample period
Fs = Fo*10
Ts = 1/Fs
# assign pre-defined variables and their functional relationship to a constant 'm'
m = ((2*L*C)-(Ts**2)/(L*C))
# describe system as a difference equation
print("\nDescribing the system as a difference equation, we have:\n y[n] = m*y[n-1] - y[n-2] \nwhere m = (2*L*C-Ts^2)/(L*C)")
print("\nor:\n a0*y[n] = b0*x[n] - a1*y[n-1] - a2*y[n-2]\nwhere b0 = 1.0, a0 = 1.0, a1 = -m, and a2 = 1.0")
# create input from unit impulse function
index = arange(0,10*Ts,Ts)
x = unit_impulse(index)
# assign coefficient arrays for input
b = array([1.0])
a = array([1.0, -1.0*m, 1.0])
y = lfilter(b, a, x)
# format and plot graph of unit impulse response
stem(index, y)
grid()
xlabel('n (sampling period = 12.5 microseconds)')
ylabel('Impulse response')
title('Impulse response of a discrete LC system')
print "\nIf sampling period Ts = 12.5 microseconds, Inductance L = 1 microHenry, and capacitance C = 4 microFarads, then"
print "m = ((2*L*C)-(Ts**2)/(L*C)) = " + str(m)
print "\nand impulse response y[n] for 1st 10 sampling periods (beginning with y[0]) = " + str(y)
show()
# calculate and assign angular frequency response using system coefficients
w,h = freqz(b,a) #w = sample frequency array, h = frequency response array
# format and plot graph of frequency response by sample frequency
plot(w/pi*(Fs/2), abs(h))
grid()
xlabel('Frequency (Hz)')
ylabel('Amplitude')
title('Frequency response of a discrete LC system')
show()
def doplot(B, A, freq = (315.0/88.0) * 8.0):
w, h = sps.freqz(B, A)
fig = plt.figure()
plt.title('Digital filter frequency response')
db = 20 * np.log10(abs(h))
for i in range(1, len(w)):
if (db[i] >= -10) and (db[i - 1] < -10):
print(">-10db crossing at ", w[i] * (freq/pi) / 2.0)
if (db[i] >= -3) and (db[i - 1] < -3):
print(">-3db crossing at ", w[i] * (freq/pi) / 2.0)
if (db[i] < -3) and (db[i - 1] >= -3):
print("<-3db crossing at ", w[i] * (freq/pi) / 2.0)
ax1 = fig.add_subplot(111)
plt.plot(w * (freq/pi) / 2.0, 20 * np.log10(abs(h)), 'b')
plt.ylabel('Amplitude [dB]', color='b')
plt.xlabel('Frequency [rad/sample]')
ax2 = ax1.twinx()
angles = np.unwrap(np.angle(h))
plt.plot(w * (freq/pi) / 2.0, angles, 'g')
plt.ylabel('Angle (radians)', color='g')
plt.grid()
plt.axis('tight')
plt.show()
def dosplot(B, A, freq = (315.0/88.0) * 8.0):
w, h = sps.freqz(B, A)
fig = plt.figure()
plt.title('Digital filter frequency response')
ax1 = fig.add_subplot(111)
db = 20 * np.log10(abs(h))
for i in range(1, len(w)):
if (db[i] >= -10) and (db[i - 1] < -10):
print(">-10db crossing at ", w[i] * (freq/pi) / 2.0)
if (db[i] >= -3) and (db[i - 1] < -3):
print("-3db crossing at ", w[i] * (freq/pi) / 2.0)
if (db[i] < -3) and (db[i - 1] >= -3):
print("<-3db crossing at ", w[i] * (freq/pi) / 2.0)
if (db[i] < -10) and (db[i - 1] >= -10):
print("<-10db crossing at ", w[i] * (freq/pi) / 2.0)
if (db[i] < -20) and (db[i - 1] >= -20):
print("<-20db crossing at ", w[i] * (freq/pi) / 2.0)
plt.plot(w * (freq/pi) / 2.0, 20 * np.log10(abs(h)), 'b')
plt.ylabel('Amplitude [dB]', color='b')
plt.xlabel('Frequency [rad/sample]')
plt.show()
x1 = -1
x2 = 1
dx = (x2 - x1) / (nw - 1)
w = zeros(nw)
for i in range(nw):
w[i] = 2.0 * pi * pow(10, x1 + i * dx)
[win, h] = signal.freqs(b, a, w)
hr = real(h)
hi = imag(h)
for i in range(len(h)):
print(" href1[%d] = std::complex<double> (%+.14lf,%+.14lf);" %
(i, hr[i], hi[i]))
nw = 41
f = linspace(0, pi, nw)
bz = asarray([
0.056340000000000, -0.000935244000000, -0.000935244000000,
0.056340000000000
])
az = asarray([
1.000000000000000, -2.129100000000000, 1.783386300000000,
-0.543463100000000
])
[fin, hz] = signal.freqz(bz, az, f)
hr = real(hz)
hi = imag(hz)
for i in range(len(fin)):
print(" href2[%d] = std::complex<double> (%+.14lf,%+.14lf);" %
(i, hr[i], hi[i]))
def generate_third_stage(header, body, third_stage_configs, combined_response,
points, input_sample_rate, stop_band_atten):
max_coefs_per_phase = 32
for config in third_stage_configs:
divider = config[0]
passband = config[1]
stopband = config[2]
name = config[3]
coefs_per_phase = config[4]
#if is_custom then use the PDM rate for making the graphs
is_custom = config[5]
pbw = passband / divider
sbw = stopband / divider
a = [1, 1, 0]
w = [1, 1, 1]
thing1 = (00.0 / 48000.0) / divider
thing2 = (200.0 / 48000.0) / divider
bands = [0, 0, thing2, pbw, sbw, 0.5]
third_stage_response, coefs = generate_stage(
coefs_per_phase * divider,
bands,
a,
w,
stopband_attenuation=stop_band_atten)
#ensure the there is never any overflow
coefs /= sum(abs(coefs))
body.write("const int g_third_stage_" + name + "_fir[" +
str(divider * (2 * max_coefs_per_phase - 1)) + "] = {\n")
header.write("extern const int g_third_stage_" + name + "_fir[" +
str(divider * (2 * max_coefs_per_phase - 1)) + "];\n")
total_abs_sum = 0
for phase in reversed(range(divider)):
body.write("//Phase " + str(phase) + "\n\t")
for i in range(coefs_per_phase):
index = coefs_per_phase * divider - divider - (i * divider -
phase)
if coefs[i] > 0.5:
print "Single coefficient too big in third stage FIR"
d_int = int(coefs[index] * 2147483647.0 * 2.0)
total_abs_sum += abs(d_int)
body.write("0x{:08x}, ".format(ctypes.c_uint(d_int).value))
if (i % 8) == 7:
body.write("\n\t")
for i in range(coefs_per_phase, max_coefs_per_phase):
body.write("0x{:08x}, ".format(ctypes.c_uint(0).value))
if (i % 8) == 7:
body.write("\n\t")
for i in range(coefs_per_phase - 1):
index = coefs_per_phase * divider - divider - (i * divider -
phase)
d_int = int(coefs[index] * 2147483647.0 * 2.0)
body.write("0x{:08x}, ".format(ctypes.c_uint(d_int).value))
if (i % 8) == 7:
body.write("\n\t")
for i in range(coefs_per_phase - 1, max_coefs_per_phase - 1):
body.write("0x{:08x}, ".format(ctypes.c_uint(0).value))
if (i % 8) == 7:
body.write("\n\t")
body.write("\n")
body.write("};\n")
#print str(total_abs_sum) + "(" + str(abs(total_abs_sum - 2147483647.0*2.0)) + ")"
if abs(total_abs_sum - 2147483647.0 * 2.0) > 32 * divider:
print "Warning: error in third stage too large"
body.write("const int fir3_" + name + "_debug[" +
str(max_coefs_per_phase * divider) + "] = {\n\t")
header.write("extern const int fir3_" + name + "_debug[" +
str(max_coefs_per_phase * divider) + "];\n")
for i in range(coefs_per_phase * divider):
body.write("{:10d}, ".format(int(2147483647.0 * coefs[i])))
if (i % 8) == 7:
body.write("\n\t")
for i in range(coefs_per_phase * divider,
max_coefs_per_phase * divider):
body.write("{:10d}, ".format(int(0)))
if (i % 8) == 7:
body.write("\n\t")
body.write("};\n")
(_, H) = signal.freqz(coefs, worN=points)
plot_response(H, 'third_stage_' + str(name))
passband_max = float('-inf')
passband_min = float('inf')
magnitude_response = []
input_freq = []
for i in range(points):
mag = combined_response[i] * abs(H[i])
freq = 0.5 * i / points
if freq < 0.5 / divider:
magnitude_response.append(mag)
if is_custom:
input_freq.append(freq * input_sample_rate)
else:
input_freq.append(freq * divider)
if freq < passband / divider:
passband_max = max(passband_max, mag)
passband_min = min(passband_min, mag)
magnitude_response /= passband_max
magnitude_response = 20 * numpy.log10(magnitude_response)
plt.clf()
plt.plot(input_freq, magnitude_response)
plt.ylabel('Magnitude Response')
if is_custom:
plt.xlabel('Frequency (kHz)')
else:
plt.xlabel('Normalised Output Freq')
plt.savefig("output_" + name + '.pdf', format='pdf', dpi=1000)
print "Filter name: " + name
print "Final stage divider: " + str(divider)
print "Output sample rate: " + str(input_sample_rate / divider) + "kHz"
print "Pass bandwidth: " + str(
input_sample_rate * passband / divider) + "kHz of " + str(
input_sample_rate / (divider * 2)) + "kHz total bandwidth."
print "Pass bandwidth(normalised): " + str(
passband * 2) + " of Nyquist."
print "Stop band start: " + str(
input_sample_rate * stopband / divider) + "kHz of " + str(
input_sample_rate / (divider * 2)) + "kHz total bandwidth."
print "Stop band start(normalised): " + str(
stopband * 2) + " of Nyquist."
print "Stop band attenuation: " + str(stop_band_atten) + "dB."
# print "(3.072MHz) Passband:" + str(48000*2*passband/divider) + "Hz Stopband:"+ str(48000*2*stopband/divider) + "Hz"
# print "(2.822MHz) Passband:" + str(44100*2*passband/divider) + "Hz Stopband:"+ str(44100*2*stopband/divider) + "Hz"
if 1.0 / passband_max > 8.0:
print "Error: Compensation factor is too large"
#The compensation factor should be in Q(5.27) format
comp_factor = ((1 << 27) - 1) / passband_max
header.write("#define FIR_COMPENSATOR_" + name.upper() + " (" +
str(int(comp_factor)) + ")\n")
header.write("\n")
print "Passband ripple = " + str(
abs(20.0 * numpy.log10(passband_min / passband_max))) + " dB\n"
return
def freqz_resp_list(b,
a=np.array([1]),
mode='dB',
fs=1.0,
Npts=1024,
fsize=(6, 4)):
"""
A method for displaying digital filter frequency response magnitude,
phase, and group delay. A plot is produced using matplotlib
freq_resp(self,mode = 'dB',Npts = 1024)
A method for displaying the filter frequency response magnitude,
phase, and group delay. A plot is produced using matplotlib
freqz_resp(b,a=[1],mode = 'dB',Npts = 1024,fsize=(6,4))
b = ndarray of numerator coefficients
a = ndarray of denominator coefficents
mode = display mode: 'dB' magnitude, 'phase' in radians, or
'groupdelay_s' in samples and 'groupdelay_t' in sec,
all versus frequency in Hz
Npts = number of points to plot; default is 1024
fsize = figure size; defult is (6,4) inches
Mark Wickert, January 2015
"""
if type(b) == list:
# We have a list of filters
N_filt = len(b)
f = np.arange(0, Npts) / (2.0 * Npts)
for n in range(N_filt):
w, H = signal.freqz(b[n], a[n], 2 * np.pi * f)
if n == 0:
plt.figure(figsize=fsize)
if mode.lower() == 'db':
plt.plot(f * fs, 20 * np.log10(np.abs(H)))
if n == N_filt - 1:
plt.xlabel('Frequency (Hz)')
plt.ylabel('Gain (dB)')
plt.title('Frequency Response - Magnitude')
elif mode.lower() == 'phase':
plt.plot(f * fs, np.angle(H))
if n == N_filt - 1:
plt.xlabel('Frequency (Hz)')
plt.ylabel('Phase (rad)')
plt.title('Frequency Response - Phase')
elif (mode.lower() == 'groupdelay_s') or (mode.lower()
== 'groupdelay_t'):
"""
Notes
-----
Since this calculation involves finding the derivative of the
phase response, care must be taken at phase wrapping points
and when the phase jumps by +/-pi, which occurs when the
amplitude response changes sign. Since the amplitude response
is zero when the sign changes, the jumps do not alter the group
delay results.
"""
theta = np.unwrap(np.angle(H))
# Since theta for an FIR filter is likely to have many pi phase
# jumps too, we unwrap a second time 2*theta and divide by 2
theta2 = np.unwrap(2 * theta) / 2.
theta_dif = np.diff(theta2)
f_diff = np.diff(f)
Tg = -np.diff(theta2) / np.diff(w)
# For gain almost zero set groupdelay = 0
idx = pylab.find(20 * np.log10(H[:-1]) < -400)
Tg[idx] = np.zeros(len(idx))
max_Tg = np.max(Tg)
#print(max_Tg)
if mode.lower() == 'groupdelay_t':
max_Tg /= fs
plt.plot(f[:-1] * fs, Tg / fs)
plt.ylim([0, 1.2 * max_Tg])
else:
plt.plot(f[:-1] * fs, Tg)
plt.ylim([0, 1.2 * max_Tg])
if n == N_filt - 1:
plt.xlabel('Frequency (Hz)')
if mode.lower() == 'groupdelay_t':
plt.ylabel('Group Delay (s)')
else:
plt.ylabel('Group Delay (samples)')
plt.title('Frequency Response - Group Delay')
else:
s1 = 'Error, mode must be "dB", "phase, '
s2 = '"groupdelay_s", or "groupdelay_t"'
print(s1 + s2)
kHz = 1000.0 # kHz
# time for creating sin wave
time = arange(0, 1, 1.0 / num_samples)
# Create frequencies to use for Signal Processing
f1 = 15000 # 15kHz
f2 = 30000 # 30kHz
# Create a Bandpass filter
numtaps = 2048
low_cutoff = 43500 # 43.5kHz
high_cutoff = 46500 # 46.5kHz
nyq_rate = sampling_rate / 2
bpf = firwin(numtaps, [low_cutoff / nyq_rate, high_cutoff / nyq_rate],
pass_zero=False)
w, h = freqz(bpf)
# Plot bandpass filter response
# plt.subplot(221)
# plot(w / (2 * pi), 20 * log10(abs(h)))
# plt.title('FIR Bandpass Filter Response')
# plt.ylabel('Magnitude (dB)')
# plt.xlabel('Frequency Coefficient')
class Prompt(cmd.Cmd):
def do_send(self, msg):
print("Sending: <", msg, ">")
sock.sendto(str.encode(msg), (host, port))
def default(self, msg):
# wpass: la frecuencia de paso normalizada
# wstop: la frecuencia de corte normalizada
# gpass: máxima atenuación tolerable en la banda de paso (en dB)
# gstop: mínima atenuación tolerable en la banda de rechazo (en dB)
# rp: amplitud de ripple tolerable en las transiciones (en dB)
orden, wn = sg.cheb1ord(wp=wpass, ws=wstop, gpass=3, gstop=40)
[coef_numerador_b, coef_denominador_a] = sg.cheby1(N=orden,
rp=3,
Wn=wn,
btype='lowpass',
output='ba')
''' Diagrama de Bode '''
# Le pasamos la frecuencia de muestreo para que el resultado lo ponga en escala de 0 a fs/2. Si no se la pasamos,
# lo devolvería normalizado y tenemos que arreglarlo luego
f, h = sg.freqz(coef_numerador_b, coef_denominador_a, fs=fs)
fig, ax1 = plt.subplots()
ax1.set_title('Filtro Chebyshev Tipo I pasa bajos')
ax1.plot(f, 20 * np.log10(abs(h)))
ax1.set_xlabel('Frecuencia [Hz]')
ax1.set_ylabel('Amplitud [dB]')
ax1.margins(0, 0.1)
ax1.grid(which='both', axis='both')
ax2 = ax1.twinx()
ax2.plot(f, np.unwrap(np.angle(h)), 'g')
ax2.set_ylabel('Fase (rad)', color='g')
senal_filtrada_ideal = filtrar_pasa_bajos_ideal(senal_ruidosa, fs, 800)
def generate_first_stage(header, body, points, pbw, sbw, first_stage_num_taps):
nulls = 1.0 / 8.0
a = [1, 0, 0, 0, 0]
w = [1, 1, 1, 1, 1]
bands = [
0, pbw, nulls * 1 - sbw, nulls * 1 + sbw, nulls * 2 - sbw,
nulls * 2 + sbw, nulls * 3 - sbw, nulls * 3 + sbw, nulls * 4 - sbw, 0.5
]
first_stage_response, coefs = generate_stage(first_stage_num_taps, bands,
a, w)
#ensure the there is never any overflow
coefs /= sum(abs(coefs))
total_abs_sum = 0
for t in range(0, len(coefs) / (8 * 2)):
header.write("extern const int g_first_stage_fir_" + str(t) +
"[256];\n")
body.write("const int g_first_stage_fir_" + str(t) + "[256] = {\n\t")
max_for_block = 0
for x in range(0, 256):
d = 0.0
for b in range(0, 8):
if (((x >> (7 - b)) & 1) == 1):
d = d + coefs[t * 8 + b]
else:
d = d - coefs[t * 8 + b]
d_int = int(d * 2147483647.0)
max_for_block = max(max_for_block, d_int)
body.write("0x{:08x}, ".format(ctypes.c_uint(d_int).value))
if (x & 7) == 7:
body.write("\n\t")
body.write("};\n\n")
total_abs_sum = total_abs_sum + max_for_block * 2
#print str(total_abs_sum) + "(" + str(abs(total_abs_sum - 2147483647.0)) + ")"
if abs(total_abs_sum - 2147483647.0) > 6:
print "Warning: error in first stage too large"
body.write("const int fir1_debug[" + str(first_stage_num_taps) +
"] = {\n\n")
header.write("extern const int fir1_debug[" + str(first_stage_num_taps) +
"];\n")
for i in range(0, len(coefs)):
body.write("{:10d}, ".format(int(2147483647.0 * coefs[i])))
if ((i & 7) == 7):
body.write("\n")
body.write("};\n")
(_, H) = signal.freqz(coefs, worN=points)
plot_response(H, 'first_stage')
[stop, passband_min,
passband_max] = measure_stopband_and_ripple(bands, a, H)
max_passband_output = int(2147483647.0 * 10.0**(passband_max / 20.0) + 1)
header.write("#define FIRST_STAGE_MAX_PASSBAND_OUTPUT (" +
str(max_passband_output) + ")\n")
header.write("\n")
return H
for i in range(2):
qz.append(z[i])
qp.append(p[i])
qk.append(k)
pylab.subplot2grid((2, 2), (1, 0), colspan=2)
pylab.title("Frequency response")
pylab.ylabel("Gain (dB)")
pylab.xlabel("Frequency (Hz)")
pylab.minorticks_on()
pylab.grid(b=True, which='major', color='b')
pylab.grid(b=True, which='minor')
(b, a) = signal.zpk2tf(original_z, original_p, original_k)
(w, h) = signal.freqz(b, a)
pylab.plot(w * fs0 / (2 * np.pi), 20 * np.log10(h))
print("A: ")
print(a)
print("B: ")
print(b)
print("qz: ")
print(qz)
print("qp: ")
print(qp)
qb, qa = signal.zpk2tf(qz, qp, np.prod(qk))
(qw, qh) = signal.freqz(qb, qa)
pylab.plot(qw * fs0 / (2 * np.pi), 20 * np.log10(qh))
pylab.show()
def preview(args):
import matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as plt
from scipy.io.wavfile import write as wavwrite
from scipy.signal import freqz
preview_dir = os.path.join(args.train_dir, 'preview')
if not os.path.isdir(preview_dir):
os.makedirs(preview_dir)
# Load graph
infer_metagraph_fp = os.path.join(args.train_dir, 'infer', 'infer.meta')
graph = tf.get_default_graph()
saver = tf.train.import_meta_graph(infer_metagraph_fp)
# Generate or restore z_i and z_o
z_fp = os.path.join(preview_dir, 'z.pkl')
if os.path.exists(z_fp):
with open(z_fp, 'rb') as f:
_zs = pickle.load(f)
else:
# Sample z
samp_feeds = {}
samp_feeds[graph.get_tensor_by_name('samp_z_n:0')] = args.preview_n
samp_fetches = {}
samp_fetches['zs'] = graph.get_tensor_by_name('samp_z:0')
with tf.Session() as sess:
_samp_fetches = sess.run(samp_fetches, samp_feeds)
_zs = _samp_fetches['zs']
# Save z
with open(z_fp, 'wb') as f:
pickle.dump(_zs, f)
# Create labels
sample_n = 20
_zs = _zs[:sample_n]
_ys = np.zeros([sample_n])
for i in range(10):
# one-hot vector
# _ys[2 * i + 1][i] = 1
# _ys[2 * i][i] = 1
# integer labels
_ys[2 * i] = 10 + i
_ys[2 * i + 1] = 10 + i
_ys = np.expand_dims(_ys, axis=1)
# Set up graph for generating preview images
feeds = {}
feeds[graph.get_tensor_by_name('z:0')] = _zs
feeds[graph.get_tensor_by_name('y:0')] = _ys
feeds[graph.get_tensor_by_name('flat_pad:0')] = _WINDOW_LEN // 2
fetches = {}
fetches['step'] = tf.train.get_or_create_global_step()
fetches['G_z'] = graph.get_tensor_by_name('G_z:0')
fetches['G_z_flat_int16'] = graph.get_tensor_by_name('G_z_flat_int16:0')
if args.wavegan_genr_pp:
fetches['pp_filter'] = graph.get_tensor_by_name(
'G/pp_filt/conv1d/kernel:0')[:, 0, 0]
# Summarize
G_z = graph.get_tensor_by_name('G_z_flat:0')
summaries = [
tf.summary.audio('preview',
tf.expand_dims(G_z, axis=0),
_FS,
max_outputs=1)
]
fetches['summaries'] = tf.summary.merge(summaries)
summary_writer = tf.summary.FileWriter(preview_dir)
# PP Summarize
if args.wavegan_genr_pp:
pp_fp = tf.placeholder(tf.string, [])
pp_bin = tf.read_file(pp_fp)
pp_png = tf.image.decode_png(pp_bin)
pp_summary = tf.summary.image('pp_filt', tf.expand_dims(pp_png,
axis=0))
# Loop, waiting for checkpoints
ckpt_fp = None
while True:
latest_ckpt_fp = tf.train.latest_checkpoint(args.train_dir)
if latest_ckpt_fp != ckpt_fp:
print('Preview: {}'.format(latest_ckpt_fp))
with tf.Session() as sess:
saver.restore(sess, latest_ckpt_fp)
_fetches = sess.run(fetches, feeds)
_step = _fetches['step']
gen_speech = _fetches['G_z_flat_int16']
gen_len = int(len(gen_speech) / sample_n)
for i in range(sample_n):
label = int(i / 2)
start = i * gen_len
end = start + gen_len
preview_fp = os.path.join(
preview_dir, '{}_{}_{}.wav'.format(str(label), str(_step),
str(i)))
wavwrite(preview_fp, _FS, gen_speech[start:end])
summary_writer.add_summary(_fetches['summaries'], _step)
if args.wavegan_genr_pp:
w, h = freqz(_fetches['pp_filter'])
fig = plt.figure()
plt.title('Digital filter frequncy response')
ax1 = fig.add_subplot(111)
plt.plot(w, 20 * np.log10(abs(h)), 'b')
plt.ylabel('Amplitude [dB]', color='b')
plt.xlabel('Frequency [rad/sample]')
ax2 = ax1.twinx()
angles = np.unwrap(np.angle(h))
plt.plot(w, angles, 'g')
plt.ylabel('Angle (radians)', color='g')
plt.grid()
plt.axis('tight')
_pp_fp = os.path.join(
preview_dir, '{}_ppfilt.png'.format(str(_step).zfill(8)))
plt.savefig(_pp_fp)
with tf.Session() as sess:
_summary = sess.run(pp_summary, {pp_fp: _pp_fp})
summary_writer.add_summary(_summary, _step)
print('Done')
ckpt_fp = latest_ckpt_fp
time.sleep(1)
def main():
t = np.arange(0, 0.01, 1 / fs)
# %% noisy sinusoid
xc = np.exp(
1j * 2 * np.pi * F *
t) + 0.01 * (np.random.randn(t.size) + 1j * np.random.randn(t.size))
xr = np.cos(2 * np.pi * F * t) + 0.01 * np.random.randn(t.size)
# %% estimate sinusoid frequency
festc, sigmac = subspace.subspace.esprit_c(xc, Ntone // 2, M, fs)
print('complex')
print(festc)
print(sigmac)
# %% real
# design filter coeff (offline, one-time)
b = remez(L, [0, 0.1, 0.15, 0.35, 0.4, 0.5], [0, 1, 0])
tic = time()
yrpy = lfilter(b, 1, xr)
tscipy = time() - tic
tic = time()
yrfort = subspace.filters.fircircfilter(xr.astype(np.float32), b)[0]
tfort = time() - tic
np.testing.assert_allclose(yrfort, yrpy,
rtol=1e-4) # single prec vs double prec
tic = time()
yr = fircirc(b, xr)
print('{:.6f} sec. using circular buffer FIR filter'.format(time() - tic))
np.testing.assert_allclose(yr, yrpy)
# %% estimations
festr, sigmar = subspace.subspace.esprit_r(yr, Ntone, M, fs)
print('real')
print(festr)
print(sigmar)
fg, axs = subplots(2, 4, sharey=False)
plotperiodogram(t, xr, fs, axs[:, 0], 'noisy input signal X')
axs[0, 0].set_ylabel('amplitude [dB]')
axs[1, 0].set_ylabel('amplitude')
plotperiodogram(t, yrpy, fs, axs[:, 1],
'Scipy lfilter() signal, {:.3f} ms'.format(tscipy * 1000))
plotperiodogram(t, yrfort, fs, axs[:, 2],
'Fortran filtered signal, {:.3f} ms'.format(tfort * 1000))
for a in axs[0, :]:
a.set_xlabel('frequency [Hz]')
a.autoscale(True, axis='x', tight=True)
a.set_ylim(-100, -20)
freq, response = freqz(b)
axs[0, -1].plot(freq * fs / (2 * np.pi), 10 * np.log10(abs(response)))
axs[0, -1].set_title(f'filter response L={L}')
axs[0, -1].set_ylim(-40, 2)
impulse = np.repeat(0., L)
impulse[0] = 1.
response = lfilter(b, 1, impulse)
axs[1, -1].plot(response)
axs[1, -1].set_xlabel('sample number')
show()
from scipy import signal
import csv
import matplotlib.pyplot as plt
import numpy as np
with open('/home/pruthvirg/Downloads/h.csv', 'r') as f:
reader = csv.reader(f)
your_list = list(reader)
w, h = signal.freqz(your_list)
fig, ax1 = plt.subplots()
ax1.set_title('Digital filter frequency response')
ax1.plot(w, abs(h), 'b')
ax1.set_ylabel('Amplitude [dB]', color='b')
ax1.set_xlabel('Frequency [rad/sample]')
ax2 = ax1.twinx()
angles = np.unwrap(np.angle(h))
ax2.plot(w, angles, 'g')
ax2.set_ylabel('Angle (radians)', color='g')
ax2.grid()
ax2.axis('tight')
plt.show()
x = np.linspace(1, 2**10, 2**10)
y = np.cos(0.2 * (np.pi) * x) + np.cos(0.85 * (np.pi) * x)
plt.plot(abs(y))
plt.title('Plot of input signal')
plt.xlabel('n')
plt.ylabel('x[n]')
plt.grid(True)
"""
FIR filter design example; requires SciPy 0.9 or later.
"""
import numpy as np
from scipy.signal import firwin2, freqz, kaiserord
from matplotlib.pylab import plot, show, grid, xlabel, ylabel, legend, title
# Bandpass with a notch.
desired_freq = [0.0, 0.1, 0.2, 0.56, 0.6, 0.64, 0.8, 0.9, 1.0]
desired_gain = [0.0, 0.0, 1.0, 1.0, 0.75, 1.0, 1.0, 0.0, 0.0]
# Use firwin2 with a Kaiser window to design the filter.
ntaps, beta = kaiserord(ripple=65, width=0.08)
taps = firwin2(ntaps, desired_freq, desired_gain, window=('kaiser', beta))
# Compute the filter's response.
w, h = freqz(taps, [1.0], worN=8000)
# Plot the desired and actual responses.
plot(desired_freq, desired_gain, 'g-', label='Desired')
plot(w/np.pi, np.abs(h), 'b', label='Computed')
xlabel('Frequency (rel. to Nyquist)')
ylabel('Gain')
title('FIR Filter Frequency Response (%d taps)' % ntaps)
legend()
grid(True)
show()
f0 = 100 # fundamental pitch of excitation impulse
nharm = 30 # number of harmonics in impulse
nsamps = 8000 # number of samples to collect
output_samples = 513 # number of samples per table (attack AND decay)
table_size = 257 # length of each wavetable
nsamps = output_samples * 11 # number of samples to process. offset = 10 cycles, + output
fs = output_samples * f0 # sample rate
nsecs = F.size
R = np.exp(-np.pi * BW / fs)
theta = 2 * np.pi * F / fs
poles = np.multiply(R, np.exp(1j * theta)) # complex poles
B = 1
polesMatrix = np.matrix([poles, np.conj(poles)])
A = np.real(np.poly(polesMatrix.A1))
w, h = signal.freqz(B, A)
"""
# plot formant filter frequency response
freqPlot = plt.figure();
plt.title('Formant Filter Frequency Response')
ax1 = freqPlot.add_subplot(111)
plt.plot(w, 20 * np.log10(abs(h)), 'b')
plt.ylabel('amplitude[dB]', color = 'b')
plt.xlabel('frequency [rad/sample]')
ax2 = ax1.twinx()
angles = np.unwrap(np.angle(h))
plt.plot(w, angles, 'g')
plt.ylabel('Angle (radians)', color='g')
plt.grid()
import sys
sys.path.append('../funcs')
from animations import *
from filters import *
from playwav import *
rate, audio = wav.read('sndfile.wav')
audio = audio[:, 1]
t = np.arange(len(audio)) / float(rate)
print 'Sampling rate: ', rate
print 'Audio shape: ', audio.shape
w, H = signal.freqz(audio)
#filter and downsample the signal no 8khz
# newSamplingRate = 8000
# downSamplingFactor = rate/newSamplingRate
samplingFactor = 4
rows = 500
cols = 512
frame = 0.0 * np.ones((rows, cols, 3))
frametxt = frame.copy()
cv2.putText(frame, "f: change filter", (20, 50), cv2.FONT_HERSHEY_SIMPLEX, 1,
(255, 128, 128))
cv2.putText(frame, "p: play audio file, s: stop", (20, 100),
cv2.FONT_HERSHEY_SIMPLEX, 1, (255, 128, 128))
if voiced[i]:
# choose alpha and gamma to get something like voiced speech
alpha1 = 0.05 * np.pi + 0.25 * np.pi * r1[0]
gamma1 = 0.9 + 0.09 * r1[1]
alpha2 = alpha1 + 0.4 * np.pi * r2[0]
gamma2 = 0.9 + 0.05 * r2[1]
gain = 10
else:
alpha1 = 0.5 * np.pi + 0.4 * np.pi * r1[0]
gamma1 = 0.8 + 0.1 * r1[1]
alpha2 = 0.5 * np.pi + 0.4 * np.pi * r2[0]
gamma2 = 0.8 + 0.1 * r2[1]
gain = 1
w1, h1 = signal.freqz(gain,
[1, -2 * gamma1 * np.cos(alpha1), gamma1 * gamma1],
range(1, L[i] + 1) * Wo[i])
w2, h2 = signal.freqz(gain,
[1, -2 * gamma2 * np.cos(alpha2), gamma2 * gamma2],
range(1, L[i] + 1) * Wo[i])
for m in range(1, L[i] + 1):
A[i, m] = np.abs(h1[m - 1] * h2[m - 1])
if voiced[i]:
phase[i, m] = np.angle(h1[m - 1] * h2[m - 1])
else:
r = np.random.rand(1)
phase[i, m] = -np.pi + r[0] * 2 * np.pi
# write to a Codec 2 model file
adc = fx.Fixed(q_adc) # adc quantizer instance
fil_ma_q = fx.FIX_filt_MA(q_mul, q_acc) # fxpoint filter instance
dac = fx.Fixed(q_dac) # dac quantizer instance
coeffq = fx.Fixed(q_coeff)
### quantize coefficients
aq = coeffq.fix(a)
bq = coeffq.fix(b)
gq = coeffq.fix(g)
if coeffq.N_over > 0:
print("Coefficient overflows:", coeffq.N_over)
### Berechnung der Übertragungsfunktion mit idealen und quantisierten Koeff.
# idealer Betragsgang
[w, Hf] = sig.freqz(b, a, worN=int(N_FFT / 2))
Hf = abs(
Hf
) * g * a_sig # Idealer Betragsgang zwischen f = 0 ... f_S/2 an N_FFT/2 Punkten
f = w / (2 * pi) * f_S # translate w to absolute frequencies
# Betragsgang mit quantisierten Koeffizienten
[w, Hfq] = sig.freqz(bq, aq, int(N_FFT / 2))
Hfq = abs(Hfq) * gq * a_sig
wtest = array(
[fsig, f_S / 2]
) * 2 * pi / f_S # Testfrequenzen f_sig und f_S/2 (dummy-Punkt, ftest muss Vektor sein)
w, H_sig_tst = sig.freqz(b, a,
wtest) # Betrag der Übertragungsfunkt. bei ftest
H_sig = abs(H_sig_tst[0]) * g * a_sig # Ideale Übertragungsfunktion bei fsig
def butter_bandpass_filter_signal_1d(signal,
lowcut,
highcut,
sample_rate,
order,
verbose=False):
r"""
Digital filter bandpass zero-phase implementation (filtfilt)
Apply a digital filter forward and backward to a signal
Args:
signal : ndarray, shape (time,)
Single input signal in time domain
lowcut : int
Lower bound filter
highcut : int
Upper bound filter
sample_rate : int
Sampling frequency
order : int, default: 4
Order of the filter
verbose : boolean, default: False
Print and plot details
Returns:
y : ndarray
Filter signal
Dependencies:
filtfilt : scipy.signal.filtfilt
butter_bandpass : function
plt : `matplotlib.pyplot` package
freqz : scipy.signal.freqz
fast_fourier_transform : function
"""
b, a = butter_bandpass(lowcut, highcut, sample_rate, order)
y = filtfilt(b, a, signal)
if verbose:
w, h = freqz(b, a)
plt.plot((sample_rate * 0.5 / np.pi) * w,
abs(h),
label="order = %d" % order)
plt.plot([0, 0.5 * sample_rate],
[np.sqrt(0.5), np.sqrt(0.5)],
'--',
label='sqrt(0.5)')
plt.xlabel('Frequency (Hz)')
plt.ylabel('Gain')
plt.grid(True)
plt.legend(loc='best')
low = max(0, lowcut - (sample_rate / 100))
high = highcut + (sample_rate / 100)
plt.xlim([low, high])
plt.ylim([0, 1.2])
plt.title('Frequency response of filter - lowcut:' + str(lowcut) +
', highcut:' + str(highcut))
plt.show()
# TIME
plt.plot(signal, label='Signal')
plt.title('Signal')
plt.show()
plt.plot(y, label='Filtered')
plt.title('Bandpass filtered')
plt.show()
# FREQ
lower_xlim = lowcut - 10 if (lowcut - 10) > 0 else 0
fast_fourier_transform(signal,
sample_rate,
plot=True,
plot_xlim=[lower_xlim, highcut + 20],
plot_label='Signal')
fast_fourier_transform(y,
sample_rate,
plot=True,
plot_xlim=[lower_xlim, highcut + 20],
plot_label='Filtered')
plt.xlim([lower_xlim, highcut + 20])
plt.ylim([0, 2])
plt.legend()
plt.xlabel('Frequency (Hz)')
plt.show()
print('Input: Signal shape', signal.shape)
print('Output: Signal shape', y.shape)
return y
def filtfft(filt, blocklen):
return sps.freqz(filt[0], filt[1], blocklen, whole=1)[1]
plt.savefig('../images/Q1_b_espectro_nfilt.png')
# Questão 2
# (a)
if PB_filt:
lp_fpass = 32.
lp_fstop = 50.3
fny = fs/2.
#wpass = fpass*2*np.pi
#wstop = fstop*2*np.pi
#wny = fny*2*np.pi
lp_ord, lp_wn = buttord(lp_fpass/fny,lp_fstop/fny,3,40)
lp_b, lp_a = butter(lp_ord, lp_wn, 'lowpass')
#lp_b, lp_a = butter(8, lp_fpass/fny, 'lowpass')
lp_w, lp_h = freqz(lp_b, lp_a, worN=len(fhz_nf),fs=fs*2*np.pi)
sig_lp = lfilter(lp_b,lp_a,mysignal)
sig_fft_lp = np.fft.rfft(sig_lp)
f_dimensionless_lp = np.fft.rfftfreq(len(sig_lp))
T = dt*N
df = 1./T
fhz_lp = f_dimensionless_lp*df*N
if plotQ2a:
fig3 = plt.figure(figsize=(14,4.5))
plt.title('Q2 (a)')
plt.xlabel('tempo [s]')
plt.ylabel('sinal ECG filtrado PB [V]')
plt.plot(t,sig_lp)
f = np.linspace(0, 80e3, 30) # frequencies for fitting the system
Hvals = FreqResp(S0, delta, f0, f) # frequency response of the 2nd order system
#%% fitting the IIR filter
Fs = 500e3 # sampling frequency
Na = 4; Nb = 4 # IIR filter order (Na - denominator, Nb - numerator)
b, a, tau = fit_filter.LSIIR(Hvals, Na, Nb, f, Fs)
#%% plot the result
fplot = np.linspace(0, 80e3, 1000) # frequency range for the plot
Hc = FreqResp(S0, delta, f0, fplot) # frequency response of the 2nd order system
Hf = freqz(b, a, 2 * np.pi * fplot / Fs)[1] # frequency response of the fitted IIR filter
Hf = Hf*np.exp(2j*np.pi*fplot/Fs*tau) # take into account the filter time delay tau
fig1 = figure(1); cla()
ax1 = fig1.add_subplot(111)
ax1.plot(fplot, db(Hc), "+",fplot, db(Hf))
ax1.legend(('System', 'LSIIR fit'))
ax1.set_xlabel("frequency / Hz",fontsize=18)
ax1.set_ylabel("freq. response amplitude / a.u.",fontsize=18)
fig2 = figure(2); cla()
ax2 = fig2.add_subplot(111)
ax2.plot(fplot, np.angle(Hc), "+",fplot, np.angle(Hf))
ax2.legend(('System', 'LSIIR fit'))
ax2.set_xlabel("frequency / Hz",fontsize=18)
ax2.set_ylabel("freq. response angle / rad",fontsize=18)
plt.plot(tim, v)
fs = 1.0 / tim[1]
n = len(t)
freqspec = np.fft.fft(v)
Hz = np.linspace(0, fs, n)
plt.figure()
plt.plot(Hz, np.abs(freqspec))
betaorder = 5 #order of the filter
bbeta, abeta = butter_bandpass(16, 31, fs, betaorder)
thetaorder = 2
btheta, atheta = butter_bandpass(4, 7, fs, thetaorder)
wbeta, hbeta = freqz(bbeta, abeta)
wtheta, htheta = freqz(btheta, atheta)
plt.figure()
plt.title('Band Pass Filter Responses')
plt.plot(fs * wbeta / (2 * np.pi), np.abs(hbeta), 'b')
plt.plot(fs * wtheta / (2 * np.pi), np.abs(htheta), 'r')
plt.xlim(0, 100)
beta = lfilter(bbeta, abeta, v)
theta = lfilter(btheta, atheta, v)
fig = plt.figure()
plt.title('Theta Signal after 3-7 Hz band pass filter')
ax = fig.add_subplot(111)
ax.plot(tim, (theta))
def glottal_pole(f, pcm, pitch, hnr, visual=False):
"""
Algorithm to extract glottal poles using complex cepstrum.
"""
fig = None
if visual:
fig = core.Figure(6)
frame = core.parameter('Frame', 0)
# Window the framed signal
frameSize = f.shape[-1]
w = core.Window(f, core.nuttall(frameSize))
if visual:
p = core.Periodogram(w)
ax1 = fig.subplot()
fig.specplot(ax1, p, pcm)
# Excitation - use the windowed frames
ac = core.Autocorrelation(w)
ar, gg = AR.ARLevinson(ac, pcm.speech_ar_order())
ex = AR.ARExcitation(w, ar, gg)
# Glottal closure. This should be near the middle as it's
# windowed.
# wsize is enough to capture two pitch periods.
# cwsize is a bigger window, zero-padded version of
# wsize to allow phase unwrapping.
mean = np.mean(pitch)
wsize = pcm.seconds_to_period(1 / mean) * 2
cwsize = 512
gci = ex.argmax(axis=-1)
g = np.zeros((len(f), cwsize))
gw = core.nuttall(wsize)
for i in range(len(f)):
beg = gci[i] - wsize / 2
end = gci[i] + wsize / 2
if (beg < 0):
end += -beg
beg = 0
elif (end > frameSize):
beg -= end - frameSize
end = frameSize
# Make sure to window the unwindowed frame
g[i][cwsize / 2 - wsize / 2:cwsize / 2 +
wsize / 2] = gw * f[i, beg:end]
# Sample frame
if fig:
sample = w[frame]
fr = fig.subplot()
fr.plot(sample / np.max(np.abs(sample)))
fr.plot(ex[frame] / np.max(np.abs(ex[frame])))
fr.set_xlim(0, frameSize)
# Define a new PCM representing the downsampled signal for complex
# cepstrum
cepFreq = core.parameter('CepFreq', 1000.0)
cepPCM = core.PulseCodeModulation(cepFreq * 2)
clbin = pcm.hertz_to_dftbin(cepFreq, cwsize)
if not int(clbin) & 1:
clbin += 1
clsize = (clbin - 1) * 2
cl = ComplexCepstrum(g, clsize)
# Maximum phase spectra
negs = ComplexSpectrum(cl, 'max')
# Convert negative spectrum to LP
order = core.parameter('Order', 2)
negp = np.abs(negs)**2
ac = core.Autocorrelation(negp, input='psd')
a, g = AR.ARLevinson(ac, order=order)
ars = AR.ARSpectrum(a, g, clsize / 2 + 1)
roots = AR.ARRoots(a)
if fig:
neg = fig.subplot()
fig.specplot(neg, np.abs(negs), cepPCM)
spec = fig.subplot()
spec.plot(10 * np.log10(np.abs(negs[frame])**2 / clsize))
spec.plot(10 * np.log10(np.abs(ars[frame])))
zpos = roots[frame, 0].real
numer = np.array([1.0, -zpos]) * np.sqrt(g[frame])
denom = np.insert(-a[frame], 0, 1)
tmp, zspec = sp.freqz(numer, denom, clsize / 2 + 1)
spec.plot(10 * np.log10(np.abs(zspec)**2))
# Default pitch range is 40-500 Hz.
#theta = [root_angle(r) for r in roots]
theta, magtd = MinPolar(roots)
loTheta = 1e-8
hiTheta = cepPCM.hertz_to_radians(500)
thRange = hiTheta - loTheta
thVar = (1.0 / hnr * thRange)**2
for i in range(len(thVar)):
if theta[i] < loTheta or theta[i] > hiTheta:
thVar[i] = 1e8
thMean = cepPCM.hertz_to_radians(mean)
# obs, obsVar, seqVar, initMean, initVar
kTheta, kTVar = core.kalman(theta, thVar, (thMean / 4)**2, thMean,
thRange**2)
# Smooth the magnitude
mVar = (1.0 / hnr)**2
# obs, obsVar, seqVar, initMean, initVar
kMag, kMVar = core.kalman(magtd, mVar, 0.01, 0.5, 1.0)
if fig:
ang = fig.subplot()
ang.plot(pitch)
iCom = []
vCom = []
iPos = []
vPos = []
for i in range(len(roots)):
if root_complex(roots[i]):
iCom.append(i)
vCom.append(cepPCM.radians_to_hertz(root_angle(roots[i])))
elif not root_negative(roots[i]):
iPos.append(i)
vPos.append(0)
ang.plot(iCom, vCom, '1')
ang.plot(iPos, vPos, '2')
kt = [cepPCM.radians_to_hertz(x) for x in kTheta]
kv = [cepPCM.radians_to_hertz(x) for x in kTheta + np.sqrt(kTVar)]
ang.plot(kt)
ang.plot(kv)
ang.set_xlim(0, len(roots))
ang.set_ylim(0, core.parameter('MaxHz', cepFreq))
magp = fig.subplot()
magp.plot(magtd)
magp.plot(kMag)
magp.plot(kMag + np.sqrt(kMVar))
magp.plot(kMag - np.sqrt(kMVar))
#magp.plot(-np.log(magtd+1e-8))
magp.set_xlim(0, len(magtd))
if fig:
pfig = plt.figure()
pax = pfig.add_axes([0.1, 0.1, 0.8, 0.8], polar=True)
pos = roots.flatten()
mag = 1 / (np.abs(pos) + 1e-8)
arg = np.angle(pos)
pax.plot(arg, mag, '3')
pax.set_rmax(5)
if fig:
plt.show()
return kTheta, kMag, cepPCM
width = abs(passband_freq - stopband_freq) / 0.5
(tap_count, beta) = kaiserord(ripple=stopband_atten, width=width)
#if len(sys.argv) > 6: tap_count = int( sys.argv[6] )
taps = firwin( numtaps = tap_count, \
cutoff = ((passband_freq+stopband_freq)/2)/0.5, \
window = ('kaiser', beta) )
#nn = 25
#taps = []
#for ii in range(0,nn): taps.append(1.0/nn)
import matplotlib.pyplot as plt
w, h = freqz(taps, worN=8000)
fig = plt.figure()
plt.title('Digital filter frequency response')
ax1 = fig.add_subplot(111)
plt.plot(w / (2 * np.pi) * 1.001, 20 * np.log10(abs(h)), 'b')
plt.ylabel('Amplitude [dB]', color='b')
plt.xlabel('Frequency [Normalized to Fs]')
#ax2 = ax1.twinx()
#angles = np.unwrap(np.angle(h)) / (2*np.pi) * 360.0
#plt.plot(w/(2*np.pi)*1.001, angles, 'g')
#plt.ylabel('Angle (degrees)', color='g')
plt.grid()
plt.axis('tight')
plt.show()
L = 0
axis([0, 2*pi*cycles, -1.1, 1.1])
savefig('../images/figure8-11', dpi=150)
if sx==6:
N = 256 # number of points for freqz
Wc = 0.2 # 3dB point
Order = 3 # filter order
# design a Butterworth filter
[b, a] = signal.butter(Order, Wc)
# calculate the frequency repsonse
[w, h] = signal.freqz(b, a, N)
# plot the results
figure()
p = subplot(2, 1, 1)
nudge_subplot(p, 0.04)
plot(arange(N)/float(N), 20*log10(abs(h)), lw=2)
title('Frequency response')
xlabel('Frequency (normalized)')
ylabel('dB')
ylim(ylim()[0], ylim()[1]+5)
grid()
p = subplot(2, 1, 2)
nudge_subplot(p, -0.02)
#=== Differentiator: needs to have zero at f = 0 # -> antisymmetric, even numtaps -> type IV #Frequency Sampling ============= #b = sig.firwin2(L, [0, 1], [0, 1], antisymmetric = True) #=== REMEZ / Parks-McClellan / Equiripple #b = sig.remez(L, [0, 0.5], [1], type = 'differentiator') #=======================================================1 # Hilbert-Transformer: zero at f = 0 and f = fS/2 # -> antisymmetric, odd numtaps b = sig.firwin2(L, [0,0.01, 0.5, 0.99, 1], [0,1, 1, 1,0], antisymmetric = True) #b = sig.remez(L, [0, 0.1, 0.11, 0.4, 0.41, 0.5], [0,1,0], [0.1,10,0.1],type = 'hilbert') b = b / sum(abs(b)) print (b) [w, H] = sig.freqz(b, a, 1024) # Translate w to physical frequencies: f = w / (2 * pi) * f_S ############## Plot the Results ######### ## Pol/Nullstellenplan figure(1) [z, p, k] = dsp.zplane(b, a) ## ----- Impulsantwort ----- figure(2) [h, td] = dsp.impz(b, a, f_S) #Impulsantwort / Koeffizienten [ml, sl, bl] = stem(td, h) plt.setp(ml, 'markerfacecolor', 'r', 'markersize', 8) title(r'Impulsantwort h[n]') ## ----- Linear frequency plot ----- figure(3) plot(f, abs(H))
if __name__ == "__main__":
import numpy as np
import matplotlib.pyplot as plt
from scipy.signal import freqz
# Sample rate and desired cutoff frequencies (in Hz).
fs = 5000.0
lowcut = 500.0
highcut = 1250.0
# Plot the frequency response for a few different orders.
plt.figure(1)
plt.clf()
for order in [3, 6, 9]:
b, a = butter_bandpass(lowcut, highcut, fs, order=order)
w, h = freqz(b, a, worN=2000)
plt.plot((fs * 0.5 / np.pi) * w, abs(h), label="order = %d" % order)
plt.plot([0, 0.5 * fs], [np.sqrt(0.5), np.sqrt(0.5)],
'--',
label='sqrt(0.5)')
plt.xlabel('Frequenz (Hz)')
plt.ylabel('Verstärkung')
plt.grid(True)
plt.legend(loc='best')
# Filter a noisy signal.
T = 0.05
nsamples = T * fs
t = np.linspace(0, T, nsamples, endpoint=False)
a = 0.02
ecg_one_lead = signals[:, 0]
fs = fields.get('fs')
nyq_frec = fs / 2
#%%
#------DISEÑO DE FILTROS y PLANTILLA-------
ripple = -0.05
atenua = -40.
#------- Notch ---------
Q = 100
wo = 30 / (fs / 2)
t = np.arange(0, n / fs, 1 / fs)
b, a = sig.iirnotch(wo, Q)
w_notch, h_notch = sig.freqz(b, a)
w_notch = w_notch / np.pi * nyq_frec
#------Pasa Bajos-------
wpb_p = 40.0 #Hz
wpb_s = 50.0 #Hz
cant_coef_pb = 201
frecs_pb = np.array([0.0, wpb_p, wpb_s, nyq_frec])
gainsDB_pb = np.array([ripple, ripple, atenua, atenua])
gains_pb = 10**(gainsDB_pb / 20)
fir_coeff_pb = sig.firls(cant_coef_pb, frecs_pb, gains_pb, fs=fs)
w_pb, hh_fir_pb = sig.freqz(fir_coeff_pb, 1)
w_pb = w_pb / np.pi * nyq_frec
def butter_lowpass_filter(data, cutoff, fs, order=5):
b, a = butter_lowpass(cutoff, fs, order=order)
y = lfilter(b, a, data)
return y
# Filter requirements.
order = 6
fs = 30.0 # sample rate, Hz
cutoff = 3.667 # desired cutoff frequency of the filter, Hz
# Get the filter coefficients so we can check its frequency response.
b, a = butter_lowpass(cutoff, fs, order)
# Plot the frequency response.
w, h = freqz(b, a, worN=8000)
plt.subplot(2, 1, 1)
plt.plot(0.5 * fs * w / np.pi, np.abs(h), 'b')
plt.plot(cutoff, 0.5 * np.sqrt(2), 'ko')
plt.axvline(cutoff, color='k')
plt.xlim(0, 0.5 * fs)
plt.title("Lowpass Filter Frequency Response")
plt.xlabel('Frequency [Hz]')
plt.grid()
# Demonstrate the use of the filter.
# First make some data to be filtered.
T = 5.0 # seconds
n = int(T * fs) # total number of samples
t = np.linspace(0, T, n, endpoint=False)
# "Noisy" data. We want to recover the 1.2 Hz signal from this.
def change_freq_res(self, init=False, redraw=False):
if self.cnp_gain is not None:
self.cnp_gain.remove()
self.cnp_gain = None
if self.cnp_ph is not None:
self.cnp_ph.remove()
self.cnp_ph = None
if init == True:
# Generate the plots from scratch and name the axes
with self.out:
if redraw == True:
# Remove the gain and phase plots
for i in range(1, len(self.axs)):
self.axs[1].remove()
self.axs.pop(1)
self.axs[0].lines[0].set_visible(self.discrete_mode)
# Add gain (and phase) plot
if self.show_phase:
self.axs.append(self.fig.add_subplot(self.gs[:1, 1]))
self.axs.append(self.fig.add_subplot(self.gs[1:, 1]))
else:
self.axs.append(self.fig.add_subplot(self.gs[:, 1]))
# Get zeros and poles from the zero pole plot
z_re, z_im = self.axs[0].lines[1].get_data()
z = z_re + 1j * z_im
p_re, p_im = self.axs[0].lines[2].get_data()
p = p_re + 1j * p_im
# Calculate the gain (C)
gaind = np.prod(1. + 0.j - z) / np.prod(1. + 0.j - p)
gainc = np.prod(-z) / np.prod(-p)
try:
if self.discrete_mode:
# Generate the transfer function
H = signal.ZerosPolesGain(z, p, gaind, dt=0.1).to_tf()
# Generate dicrete frequency response
w, h = signal.freqz(H.num, H.den, whole=True)
# Shift the angles to [-pi, pi]
w = w - np.pi
# Shift the gain and phase accordingly
h_ph = np.fft.fftshift(np.angle(h, deg=True))
h = np.abs(np.fft.fftshift(h))
if self.show_dB:
h = 20 * np.log10(h)
else:
# Generate the transfer function
H = signal.ZerosPolesGain(z, p, gainc)
# Generate the continuous frequency response
w1, h11 = signal.freqresp(H, w=None, n=1000)
h_ph1 = np.angle(h11, deg=True)
h1 = np.abs(h11)
w2 = np.flip(-w1)
w2, h21 = signal.freqresp(H, w2, n=1000)
h_ph2 = np.angle(h21, deg=True)
h2 = np.abs(h21)
w = np.concatenate((w2, w1))
h = np.concatenate((h2, h1))
if self.show_dB:
h = 20 * np.log10(h)
h_ph = np.concatenate((h_ph2, h_ph1))
except ValueError:
w = 1
h = 1
h_ph = 1
self.calc_not_possible()
if np.any(np.isinf(h)) or np.any(np.isnan(h)) or np.any(
np.isinf(h_ph)) or np.any(np.isnan(h_ph)):
w = 1
h = 1
h_ph = 1
self.calc_not_possible()
#This is to check if any pole is on/outside of the unit circle
if np.any(np.abs(p) >= 1):
self.tx_deb.set_text("Filter is non causal")
else:
self.tx_deb.set_text("")
if init == True:
with self.out:
# Gain
self.axs[1].set_title('Frequency response')
if self.discrete_mode:
self.axs[1].plot(w, h)
else:
self.axs[1].plot(w, h)
self.axs[1].set_xlabel('$\omega$ [rad]')
self.axs[1].set_ylabel(
'|H(z)| [dB]' if self.show_dB else '|H(z)|')
# Phase
if self.show_phase:
if self.discrete_mode:
self.axs[2].plot(w, h_ph)
else:
self.axs[2].plot(w, h_ph)
self.axs[2].set_xlabel('$\omega$ [rad]')
self.axs[2].set_ylabel('$\phi$(H(z)) [deg]')
if self.discrete_mode:
positions = [-np.pi, -np.pi / 2, 0, np.pi / 2, np.pi]
labels = [
'-$\pi$', '-$\dfrac{\pi}{2}$', '0', '$\dfrac{\pi}{2}$',
'$\pi$'
]
self.axs[1].set_xticks(positions)
self.axs[1].set_xticklabels(labels)
# Move y axis to the right
self.axs[1].yaxis.set_label_position("right")
self.axs[1].yaxis.tick_right()
if self.show_phase:
self.axs[1].xaxis.set_visible(False)
positions = [-np.pi, -np.pi / 2, 0, np.pi / 2, np.pi]
labels = [
'-$\pi$', '-$\dfrac{\pi}{2}$', '0',
'$\dfrac{\pi}{2}$', '$\pi$'
]
self.axs[2].set_xticks(positions)
self.axs[2].set_xticklabels(labels)
# Move y axis to the right
self.axs[2].yaxis.set_label_position("right")
self.axs[2].yaxis.tick_right()
else:
w_max = np.round(np.max(w) / np.pi) * np.pi
w_min = np.round(np.min(w) / np.pi) * np.pi
t = np.linspace(w_min, w_max,
int((w_max - w_min) // np.pi) + 1)
t_labels = [
f'{int(np.round(tick/np.pi))}$\pi$'
if abs(int(np.round(tick / np.pi))) > 1 else
'$\pi$' if tick > 0 else
'$-\pi$' if int(np.round(tick / np.pi)) != 0 else '0'
for tick in t
]
self.axs[1].set_xticks(t)
self.axs[1].set_xticklabels(t_labels)
if self.show_phase:
self.axs[1].xaxis.set_visible(False)
self.axs[2].set_xticks(t)
self.axs[2].set_xticklabels(t_labels)
else:
# Only change the values of the plots
# Gain
self.axs[1].lines[0].set_data(w, h)
h_min = np.min(h)
h_max = np.max(h)
h_range = abs(h_max - h_min)
self.axs[1].set_ylim(
[h_min - 0.05 * h_range, h_max +
0.05 * h_range] if h_min != h_max else [h_min - 1, h_max + 1])
# Phase
if self.show_phase:
h_ph_min = np.min(h_ph)
h_ph_max = np.max(h_ph)
h_ph_range = abs(h_ph_max - h_ph_min)
self.axs[2].lines[0].set_data(w, h_ph)
self.axs[2].set_ylim([
h_ph_min - 0.05 * h_ph_range, h_ph_max + 0.05 * h_ph_range
] if h_ph_min != h_ph_max else [h_ph_min - 1, h_ph_max + 1])
# self.axs[2].set_xlim([w_min-0.05*w_range, w_max+0.05*w_range] if w_min != w_max and check else [w_min, w_max+1])
if self.active_line is not None:
l_x, l_y = self.axs[0].lines[self.active_line + 1].get_data()
if len(l_y) > self.active_point and len(
l_x) > self.active_point:
self.actual_change = False
self.lastzeroRe = round(l_x[self.active_point], 3)
self.input_Zero_RE.value = self.lastzeroRe
self.lastzeroIm = round(l_y[self.active_point], 3)
self.input_Zero_IM.value = self.lastzeroIm
self.actual_change = True
def calculate_Pst(data):
show_time_signals = 0 #Aktivierung des Plots der Zeitsignale im Flickermeter
show_filter_responses = 0 #Aktivierung des Plots der Amplitudengänge der Filter.
#(zu Prüfzecken der internen Filter)
fs = 4000
## Block 1: Modulierung des Spannungssignals
u = data - np.mean(data) # entfernt DC-Anteil
u_rms = np.sqrt(np.mean(np.power(u,2))) # Normierung des Eingangssignals
u = u / (u_rms * np.sqrt(2))
## Block 2: Quadratischer Demulator
u_0 = u**2
## Block 3: Hochpass-, Tiefpass- und Gewichtungsfilter
# Konfiguration der Filter
HIGHPASS_ORDER = 1 #Ordnungszahl der Hochpassfilters
HIGHPASS_CUTOFF = 0.05 #Hz Grenzfrequenz
LOWPASS_ORDER = 6 #Ordnungszahl des Tiefpassfilters
if (f_line == 50):
LOWPASS_CUTOFF = 35.0 #Hz Grenzfrequenz
if (f_line == 60):
LOWPASS_CUTOFF = 42.0 #Hz Grenzfrequenz
# subtract DC component to limit filter transients at start of simulation
u_0_ac = u_0 - np.mean(u_0)
b_hp, a_hp = signal.butter(HIGHPASS_ORDER, (HIGHPASS_CUTOFF/(fs/2)), 'highpass')
u_hp = signal.lfilter(b_hp, a_hp, u_0_ac)
# smooth start of signal to avoid filter transient at start of simulation
smooth_limit = min(round(fs / 10), len(u_hp))
u_hp[ : smooth_limit] = u_hp[ : smooth_limit] * np.linspace(0, 1, smooth_limit)
b_bw, a_bw = signal.butter(LOWPASS_ORDER, (LOWPASS_CUTOFF/(fs/2)), 'lowpass')
u_bw = signal.lfilter(b_bw, a_bw, u_hp)
# Gewichtungsfilter (Werte sind aus der Norm)
if (f_line == 50):
K = 1.74802
LAMBDA = 2 * np.pi * 4.05981
OMEGA1 = 2 * np.pi * 9.15494
OMEGA2 = 2 * np.pi * 2.27979
OMEGA3 = 2 * np.pi * 1.22535
OMEGA4 = 2 * np.pi * 21.9
if (f_line == 60):
K = 1.6357
LAMBDA = 2 * np.pi * 4.167375
OMEGA1 = 2 * np.pi * 9.077169
OMEGA2 = 2 * np.pi * 2.939902
OMEGA3 = 2 * np.pi * 1.394468
OMEGA4 = 2 * np.pi * 17.31512
num1 = [K * OMEGA1, 0]
denum1 = [1, 2 * LAMBDA, OMEGA1**2]
num2 = [1 / OMEGA2, 1]
denum2 = [1 / (OMEGA3 * OMEGA4), 1 / OMEGA3 + 1 / OMEGA4, 1]
b_w, a_w = signal.bilinear(np.convolve(num1, num2), np.convolve(denum1, denum2), fs)
u_w = signal.lfilter(b_w, a_w, u_bw)
## Block 4: Quadrierung und Varianzschätzer
LOWPASS_2_ORDER = 1
LOWPASS_2_CUTOFF = 1 / (2 * np.pi * 300e-3) # Zeitkonstante 300 msek.
SCALING_FACTOR = 1238400 # Skalierung des Signals auf eine Wahrnehmbarkeitsskala
u_q = u_w**2
b_lp, a_lp = signal.butter(LOWPASS_2_ORDER, (LOWPASS_2_CUTOFF/(fs/2)), 'low')
s = SCALING_FACTOR * signal.lfilter(b_lp, a_lp, u_q)
## Block 5: Statistische Berechnung
p_50s = np.mean([np.percentile(s, 100-30, interpolation="linear"),
np.percentile(s, 100-50, interpolation="linear"),
np.percentile(s, 100-80, interpolation="linear")])
p_10s = np.mean([np.percentile(s, 100-6, interpolation="linear"),
np.percentile(s, 100-8, interpolation="linear"),
np.percentile(s, 100-10, interpolation="linear"),
np.percentile(s, 100-13, interpolation="linear"),
np.percentile(s, 100-17, interpolation="linear")])
p_3s = np.mean([np.percentile(s, 100-2.2, interpolation="linear"),
np.percentile(s, 100-3, interpolation="linear"),
np.percentile(s, 100-4, interpolation="linear")])
p_1s = np.mean([np.percentile(s, 100-0.7, interpolation="linear"),
np.percentile(s, 100-1, interpolation="linear"),
np.percentile(s, 100-1.5, interpolation="linear")])
p_0_1s = np.percentile(s, 100-0.1, interpolation="linear")
P_st = np.sqrt(0.0314*p_0_1s+0.0525*p_1s+0.0657*p_3s+0.28*p_10s+0.08*p_50s)
if (show_time_signals):
t = np.linspace(0, len(u) / fs, num=len(u))
plt.figure()
plt.clf()
#plt.subplot(2, 2, 1)
plt.hold(True)
plt.plot(t, u, 'b', label="u")
plt.plot(t, u_0, 'm', label="u_0")
plt.plot(t, u_hp, 'r', label="u_hp")
plt.xlim(0, len(u)/fs)
plt.hold(False)
plt.legend(loc=1)
plt.grid(True)
#plt.subplot(2, 2, 2)
plt.figure()
plt.clf()
plt.hold(True)
plt.plot(t, u_bw, 'b', label="u_bw")
plt.plot(t, u_w, 'm', label="u_w")
plt.xlim(0, len(u)/fs)
plt.legend(loc=1)
plt.hold(False)
plt.grid(True)
#plt.subplot(2, 2, 3)
plt.figure()
plt.clf()
plt.plot(t, u_q, 'b', label="u_q")
plt.xlim(0, len(u)/fs)
plt.legend(loc=1)
plt.grid(True)
#plt.subplot(2, 2, 4)
plt.figure()
plt.clf()
plt.plot(t, s, 'b', label="s")
plt.xlim(0, len(u)/fs)
plt.legend(loc=1)
plt.grid(True)
if (show_filter_responses):
f, h_hp = signal.freqz(b_hp, a_hp, 4096)
f, h_bw = signal.freqz(b_bw, a_bw, 4096)
f, h_w = signal.freqz(b_w, a_w, 4096)
f, h_lp = signal.freqz(b_lp, a_lp, 4096)
f = f/np.pi*fs/2
plt.figure()
plt.clf()
plt.hold(True)
plt.plot(f, abs(h_hp), 'b', label="Hochpass 1. Ordnung")
plt.plot(f, abs(h_bw), 'r', label="Butterworth Tiefpass 6.Ordnung")
plt.plot(f, abs(h_w), 'g', label="Gewichtungsfilter")
plt.plot(f, abs(h_lp), 'm', label="Varianzschätzer")
plt.legend(bbox_to_anchor=(1., 1.), loc=2)
plt.hold(False)
plt.grid(True)
plt.axis([0, 35, 0, 1])
return P_st
__author__ = 'caocongcong'
from primary_signal.const_value import constValue
import scipy.signal as signal
import pylab as plt
import numpy as np
if __name__ == "__main__":
b = np.array(constValue.lp_fs400_Overband20)
w, h = signal.freqz(b, 1)
plt.plot(w / 2 / np.pi, 20 * np.log10(np.abs(h)))
plt.show()
# 进行滤波实验
fs = 1.2e9
f1 = 0.2e9
f2 = 0.5e9
time = 0.000001
t = np.linspace(0, time, int(time * fs))
s = np.sin(2 * np.pi * f1 * t) + np.sin(2 * np.pi * f2 * t)
plt.plot(t, s)
plt.xlabel('time/s')
plt.title('before fliter')
plt.show()
sf = signal.filtfilt(b, 1, s)
plt.plot(t, sf)
plt.xlabel('time/s')
plt.title('after fliter')
plt.show()