def compare_tf(a, b, ax=None, fs=44100, to_file=None):
if not ax:
fig = plt.figure(figsize=(8, 4))
ax = plt.gca()
# convert eq params to second order sections
sosA = params2sos(denormalize_params(a), fs)
sosB = params2sos(denormalize_params(b), fs)
# calcuate filter responses
fA, hA = sg.sosfreqz(sosA, worN=1024, fs=fs)
fB, hB = sg.sosfreqz(sosB, worN=1024, fs=fs)
mse = np.mean((np.abs(hA) - np.abs(hB))**2)
# plot the magnitude respose
plt.title(f"MSE: {mse:0.5f}")
original, = plt.semilogx(fA, 20 * np.log10(abs(hA)), 'r--')
reconstructed, = plt.semilogx(fB, 20 * np.log10(abs(hB)), 'b')
ax.legend(handles=[original, reconstructed],
labels=['Original', 'Reconstructed'])
ax.set_ylabel('Amplitude [dB]', color='b')
ax.set_xlabel('Frequency [Hz]')
locmaj = ticker.LogLocator(base=10, numticks=12)
ax.xaxis.set_major_locator(locmaj)
ax.set_xlim([22.0, 20000.0])
ax.set_ylim([-20, 20])
plt.grid() # note: make this look prettier
if to_file:
plt.savefig(to_file)
return fig
def main():
#SET
FS = 44100
sampleRate, inputArray = wavfile.read("test.wav")
#GET FROM USER
print("LPF================================")
F0 = 4000
Q = 3
W0 = 2 * math.pi * (F0 / FS)
sos1 = lowpass(W0, Q)
inputArray2 = signal.sosfilt(sos1, inputArray)
print("Low Shelf================================")
F0 = 3000
Q = 3
A = 1
W0 = 2 * math.pi * (F0 / FS)
sos2 = lowShelf(W0, Q, A)
inputArray3 = signal.sosfilt(sos2, inputArray2)
print("Peaking EQ================================")
F0 = 1000
Q = 3
A = 1
W0 = 2 * math.pi * (F0 / FS)
sos3 = peaking(W0, Q, A)
inputArray4 = signal.sosfilt(sos3, inputArray3)
print("High Shelf================================")
F0 = 250
Q = 3
A = 1
W0 = 2 * math.pi * (F0 / FS)
sos4 = highShelf(W0, Q, A)
inputArray5 = signal.sosfilt(sos4, inputArray4)
print("HPF================================")
F0 = 20
Q = 3
W0 = 2 * math.pi * (F0 / FS)
sos5 = highpass(W0, Q)
outputArray = signal.sosfilt(sos5, inputArray5)
w, h1 = signal.sosfreqz(sos1)
w, h2 = signal.sosfreqz(sos2)
w, h3 = signal.sosfreqz(sos3)
w, h4 = signal.sosfreqz(sos4)
w, h5 = signal.sosfreqz(sos5)
db = 20 * np.log10(np.maximum(np.abs(h1 * h2 * h3 * h3 * h4 * h5), 1e-5))
plt.plot(w / np.pi, db)
plt.show()
#CALCULATE
#READ IN AN AUDIO FILE to a np array inputArray
wavfile.write("processed.wav", sampleRate, outputArray)
def mse_tf(a, b, fs=44100):
# convert eq params to second order sections
sosA = params2sos(denormalize_params(a), fs)
sosB = params2sos(denormalize_params(b), fs)
# calcuate filter responses
fA, hA = sg.sosfreqz(sosA, worN=512, fs=fs)
fB, hB = sg.sosfreqz(sosB, worN=512, fs=fs)
return np.mean((np.abs(hA) - np.abs(hB))**2)
def make_digital_filter(N, rp, rs, Wn, btype='low'):
finish = False
WnAdd = Wn
rpAdd = rp
rsAdd = rs
fullArray = []
try:
while (finish == False):
if (WnAdd < 0.5):
WnAdd = WnAdd + 0.001
elif (abs(rpAdd - rp) / rp < 0.05):
rpAdd = rpAdd + 0.01
elif (abs(rsAdd - rs) / rs < 0.05):
rsAdd = rsAdd + 0.01
else:
raise Exception(
"There is no filters with these characteristics.")
b, a = signal.ellip(N, rpAdd, rsAdd, WnAdd, btype, analog=False)
sos = signal.tf2sos(b, a)
#print sos
w, h = signal.sosfreqz(sos, worN=1000000)
#plot_2nd_order_from_sos(sos)
makeCallibration(sos)
#plot_2nd_order_from_sos(sos)
#print "sos"
print sos
w, h = signal.sosfreqz(sos, worN=1000000)
#plot_sosfreqz(w,h)
#fullArray = getCoefficientsForElliptic(sos, True)
fullArray = getCoefficients(sos)
#print fullArray
try:
new_sos = getSosFromCoefficients(fullArray)
#new_sos = getSosFromCoefficientsForElliptic(fullArray)
finish = True
except ValueError as e:
pass
except Exception as e:
print e
print "There is no filters with these characteristics."
return
w, h = signal.sosfreqz(sos, worN=1000000)
#plot_sosfreqz(w,h)
print "new_sos"
print new_sos
print "general_coefficients"
fullArrayRounded = getRoundCoefficients(fullArray)
getKeysFromKoefArray(fullArrayRounded)
w, h = signal.sosfreqz(new_sos, worN=1000000)
plot_sosfreqz(w, h)
def butter_bandpass_filter(data,
low_cut_freq,
high_cut_freq,
Fs=params.Fs,
order=5):
"""
:param data: the samples to filter
:param low_cut_freq: the low cut frequency
:param high_cut_freq: the high cut frequency
:param Fs: the sampling frequency
:param order: the order of the filter
:return: the filtered samples
"""
sos = butter_bandpass(low_cut_freq, high_cut_freq, Fs, order=order)
y = sosfilt(sos, data)
if params.plots:
w, h = sosfreqz(sos, worN=2000)
plt.plot((Fs * 0.5 / np.pi) * w, abs(h), label="order = %d" % order)
plt.title("Output of butter bandpass")
plt.xlabel('Frequency (Hz)')
plt.ylabel('Gain')
plt.grid(True)
plt.legend(loc='best')
plt.show()
return y
def butter_highpass_fs(sig, lowcut, fs, order=5, output='ba'):
sos = signal.butter(order, [lowcut],
btype='highpass',
output=output,
fs=fs)
filtered = signal.sosfreqz(sos, worN=sig)
return filtered
def D_Filter(l_F, h_F, fs, o_filt):
# Ambos filtros son digitales
#b, a = signal.iirfilter(o_filt, Wn=[l_F/fs, h_F/fs], btype='bandpass', analog=False, ftype='butter', output='ba') ### Diseño utilizando las frecuencias normalizadas, no se le especifica Frecuencias de sampling
sos = signal.iirfilter(o_filt,
Wn=[l_F, h_F],
btype='bandpass',
ftype='butter',
analog=False,
output='sos',
fs=fs)
## Se manda a graficar utilizando sosfreqz
w, h = signal.sosfreqz(sos, 2000, fs=fs)
plt.figure(1)
Fig_Filtro = plt.subplot(2, 1, 1)
Fig_Filtro.set_title('Digital filter frequency response')
Fig_Filtro.semilogx(w, 20 * np.log10(np.maximum(abs(h), 1e-5)))
Fig_Filtro.set_ylabel('Amplitude Response [dB]')
Fig_Filtro.set_xlabel('Frequency [Hz]')
Fig_Filtro.grid()
Fig_Filtro = plt.subplot(2, 1, 2)
Fig_Filtro.semilogx(w, np.angle(h))
Fig_Filtro.set_ylabel('Phase [Degrees]')
Fig_Filtro.set_xlabel('Frequency [Hz]')
return sos
def _recv_decode_init(self, recv_f):
self._filters = []
for i in range(2):
f = recv_f[i]
filter_bp = signal.iirfilter(4, [f / 1.05, f * 1.05],
rs=40,
btype='bandpass',
analog=False,
ftype='butter',
fs=sample_f,
output='sos')
self._filters.append(filter_bp)
if not plot_spectrum:
return
import matplotlib.pyplot as plt
plt.figure()
plt.ylim(-100, 5)
plt.xlim(0, 5500)
plt.grid(True)
plt.xlabel('Frequency (Hz)')
plt.ylabel('Gain (dB)')
plt.title('{}Hz, {}Hz'.format(recv_f[0], recv_f[1]))
for i in range(2):
f = recv_f[i]
w, h = signal.sosfreqz(self._filters[i], 2000, fs=sample_f)
plt.plot(w, 20 * np.log10(np.abs(h)), label=str(f) + 'Hz')
plt.plot((f, f), (10, -100), color='red', linestyle='dashed')
plt.plot((500, 500), (10, -100), color='blue', linestyle='dashed')
plt.plot((700, 700), (10, -100), color='blue', linestyle='dashed')
plt.show()
def filt(data,
fs,
cutoff_low=None,
cutoff_high=None,
filt_type='low',
order=5):
nyq = 0.5 * fs
if cutoff_low is not None:
norm_cutoff_low = cutoff_low / nyq
if cutoff_high is not None:
norm_cutoff_high = cutoff_high / nyq
if filt_type is 'low':
#b, a = butter(order, norm_cutoff_high, btype='low', analog=False)
sos = butter(order,
norm_cutoff_high,
btype='low',
output='sos',
analog=False)
elif filt_type is 'band':
# b, a = butter(order,
# [norm_cutoff_low, norm_cutoff_high],
# btype='band',
# analog=False)
sos = butter(order, [norm_cutoff_low, norm_cutoff_high],
btype='band',
output='sos',
analog=False)
#data_filt = lfilter(b, a, data)
# note that the order is twice as passed since filter applied 2 directions
data_filt = sosfiltfilt(sos, data)
# w, h = freqz(b, a) #for showing freq response
w, h = sosfreqz(sos, fs=fs, worN=2000)
return data_filt, (w, h)
def BandPassFilter(data, lowcut, highcut, fs, order, bWindowData):
nyq = 0.5 * fs
low = lowcut / nyq
high = highcut / nyq
b, a = butter(order, [low, high], btype='band')
b = b / a[0]
a = a / a[0]
#For higher order filters use second order signal
sos = butter(6, [low, high], btype='bandpass', output='sos')
w, h = sosfreqz(sos, round(fs / 2))
if bWindowData == True:
#Uss a blackman window accross the data
window = blackman(len(data))
data = data * window
#w, h = freqz(b, a, round(fs/2))
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('Frequency (Hz)')
plt.ylabel('Gain')
plt.grid(True)
plt.legend(loc='best')
plt.show()
fData = lfilter(b, a, data)
return fData
def makefiltersos(sr,fp,fs,gp=3,gs=20): """ Wrapper function around scipy filter functions. Makes it convenient by providing frequency parameters in terms of frequencies in Hz. INPUT: sr - sampling rate in Hz. fp - pass frequency in Hz fs - stop frequency in Hz gp - pass band ripple in dB, default 3 dB gs - stop band attenuation in dB, default 20 dB doPlot - make a plot of filter gain versus frequency, default 'no' OUTPUT: sos filter coefficients. w,h for making bode plot Automatically detects the type of filter. if fp < fs the filter is low pass but if fp > fs the filter is highpass. """ # #set up filter parameters fn = sr/2 wp = fp/fn ws = fs/fn #get the filter order n,wn = signal.buttord(wp,ws,gp,gs); #design the filter #lowpass if fp < fs: sos = signal.butter(n,wn,btype='lowpass',output='sos') #highpass if fs < fp: sos = signal.butter(n,wn,btype='highpass',output='sos') #get filter respons function w,h = signal.sosfreqz(sos,fs=sr) return sos,w,h
def plotSos(sos, oversample, fs, worN=2048):
fig, ax = plt.subplots(3, 1)
fig.set_size_inches(6, 8)
fig.set_tight_layout(True)
ax[0].set_title("Amplitude Response")
ax[0].set_ylabel("Amplitude [dB]")
ax[1].set_title("Phase Response")
ax[1].set_ylabel("Phase [rad]")
ax[2].set_title("Group Delay")
ax[2].set_ylabel("Group Delay [sample]")
ax[2].set_xlabel("Frequency [rad/sample]")
cmap = plt.get_cmap("plasma")
freq, h0 = signal.sosfreqz(sos, worN=worN, fs=oversample * fs)
b, a = signal.sos2tf(sos)
_, gd = signal.group_delay((b, a), w=worN)
ax[0].plot(freq, ampToDecibel(h0), alpha=0.75, color="black")
ax[0].set_ylim((-140, 5))
ax[1].plot(freq, np.unwrap(np.angle(h0)), alpha=0.75, color="black")
ax[2].plot(freq, gd, alpha=0.75, color="black")
for axis in ax:
# axis.set_xscale("log")
axis.grid(which="both")
plt.show()
def _showfilter(sos, freq, freq_u, freq_d, fs, factor):
wn = 8192
w = np.zeros([wn, len(freq)])
h = np.zeros([wn, len(freq)], dtype=np.complex_)
for idx in range(len(freq)):
fsd = fs / factor[idx] # New sampling rate
w[:, idx], h[:, idx] = signal.sosfreqz(sos[idx],
worN=wn,
whole=False,
fs=fsd)
fig, ax = plt.subplots()
ax.semilogx(w, 20 * np.log10(abs(h) + np.finfo(float).eps), 'b')
ax.grid(which='major')
ax.grid(which='minor', linestyle=':')
ax.set_xlabel(r'Frequency [Hz]')
ax.set_ylabel('Amplitude [dB]')
ax.set_title('Second-Order Sections - Butterworth Filter')
plt.xlim(freq_d[0] * 0.8, freq_u[-1] * 1.2)
plt.ylim(-4, 1)
ax.set_xticks([16, 31.5, 63, 125, 250, 500, 1000, 2000, 4000, 8000, 16000])
ax.set_xticklabels([
'16', '31.5', '63', '125', '250', '500', '1k', '2k', '4k', '8k', '16k'
])
plt.show()
def butter_bandpass(sig, lowcut, highcut, fs, order=5, output='ob'):
nyq = 0.5 * fs
low = lowcut / nyq
high = highcut / nyq
sos = signal.butter(order, [low, high], btype='bandpass', output=output)
filtered = signal.sosfreqz(sos, sig)
return filtered
def subplot_tf(x, fs, ax, zeroline=True, ticks=False, denorm=True):
if denorm:
x = denormalize_params(x)
# convert eq params to second order sections
sos = params2sos(x, fs)
# calculate filter response
f, h = sg.sosfreqz(sos, worN=2048, fs=fs)
# plot the magnitude respose
ax.plot(f, 20 * np.log10(abs(h)), 'b')
ax.set_xscale('log')
ax.set_xlim([20.0, 20000.0])
ax.set_ylim([-20, 20])
if ticks:
ocmaj = ticker.LogLocator(base=10, numticks=12)
ax.xaxis.set_major_locator(locmaj)
else:
ax.get_xaxis().set_visible(False)
ax.get_yaxis().set_visible(False)
if zeroline:
ax.axhline(linewidth=0.5, color='gray', zorder=0)
ax.tick_params(labelbottom=False, labelleft=False)
plt.grid(False, which='both')
def plot_tf(x, fs=44100, plot_title=None, to_file=""):
if not plot_title:
plot_title = 'Digital filter frequency response'
# convert eq params to second order sections
sos = params2sos(x, fs)
# calculate filter response
f, h = sg.sosfreqz(sos, worN=2048, fs=fs)
# plot the magnitude respose
fig, ax1 = plt.subplots()
ax1.set_title(plot_title)
ax1.semilogx(f, 20 * np.log10(abs(h)), 'b')
ax1.set_ylabel('Amplitude [dB]', color='b')
ax1.set_xlabel('Frequency [Hz]')
ax1.set_xlim([22.0, 20000.0])
ax1.set_ylim([-20, 20])
ax1.grid() # note: make this look prettier
if to_file:
plt.savefig(to_file)
else:
plt.show()
plt.close()
def test_bandpass_filterbank():
f0 = 125.0 / 2.0
fs = 16000
bands, fc = pra.octave_bands(f0)
filters = pra.bandpass_filterbank(bands, fs=fs, order=16)
res = None
for sos, f in zip(filters, fc):
w, h = sosfreqz(sos, worN=4096, whole=False)
# inspect the cumulative response
if res is None:
res = np.abs(h)**2
else:
res += np.abs(h)**2
# check automatically that the cumulative response is (nearly) flat
freq = w / np.pi * fs / 2
I = np.where(
np.logical_and(freq > fc[0],
freq < np.minimum(fc[-1], 0.95 * fs / 2)))[0]
err = np.max(np.abs(10 * np.log10(res[I])))
assert err <= tol, "Bandpass filterbank test fails (err {} > tol {})".format(
err, tol)
def envelope_modifier_spread(env, m):
#env = np.array(env)
nt = len(env[0])
new_env = np.zeros((len(env), nt))
if m['synthesis']['carrier'] != 'sin':
raise ValueError(
"[vocoder] Envelope modifier 'spread' only works with sinewave carriers."
)
f = m['synthesis']['f']
nf = len(f)
for i, e in enumerate(env):
_, h = signal.sosfreqz(m['synthesis_filters']['filters'][i],
worN=f,
whole=False,
fs=m['fs'])
h = np.abs(h)
if m['synthesis_filters']['method']['zero-phase']:
h = h**2.
new_env += np.tile(h.reshape(-1, 1),
(1, nt)) * np.tile(e.reshape(1, -1), (nf, 1))
return new_env
def getRRInterval(data):
x=data
for order in [1, 2, 4, 6, 8]:
sos = qrs_detection.butter_bandpass(LOWCUT, HIGHCUT, FS, order=order)
w, h = sosfreqz(sos, worN=2000)
# Calculate time values in seconds
#times = np.arange(x.shape[0], dtype='float') / fs
y = qrs_detection.butter_bandpass_forward_backward_filter(x, LOWCUT, HIGHCUT, FS, order=4)
# Derivative - provides QRS slope information.
differentiated_ecg_measurements = np.ediff1d(y)
# Squaring - intensifies values received in derivative.
# This helps restrict false positives caused by T waves with higher than usual spectral energies..
squared_ecg_measurements = differentiated_ecg_measurements ** 2
# Moving-window integration.
integration_window = 50 # Change proportionally when adjusting frequency (in samples)
integrated_ecg_measurements = np.convolve(squared_ecg_measurements, np.ones(integration_window))
# Fiducial mark - peak detection on integrated measurements.
rpeaks = qrs_detection.pan_tompkins_detector(data, integrated_ecg_measurements, FS, integration_window)
# RR Interval
rr = np.diff(rpeaks) / FS * 1000 # in miliseconds
#hr = 60 * 1000 / rr
return rr
def butter_lowpass(sig, lowcut, highcut, fs, order=5, output='ob'):
nyq = 0.5 * fs
low = lowcut / nyq
high = highcut / nyq
sos = signal.butter(order, [high], btype='lowpass', output='ba')
filtered = signal.sosfreqz(sos, sig)
# pp = plt.semilogx((fs * 0.5 / np.pi) * w, abs(h), label=label)
return filtered
def update_frequency_response(self):
self.sos = self.get_second_order_sections()
w, h = signal.sosfreqz(self.sos,
self.normalized_frequencies * np.pi * 2)
magnitude = np.abs(h)
self.total_response_magnitude.setData(x=self.normalized_frequencies *
SAMPLERATE,
y=magnitude)
def get_plot_data(self, plot_type):
if plot_type == "Original Data":
if type(self.app_data.data) == np.ndarray:
return self.app_data.data
else:
raise ValueError("Error: Must import data first.")
elif plot_type == "Filtered Data":
if self.app_data.filter_applied:
return self.app_data.filtered_data
else:
raise ValueError("Must apply a filter first.")
elif plot_type == "FFT":
if type(self.app_data.data) == np.ndarray:
if self.app_data.filter_type == "FIR Filter" or self.app_data.filter_type == "Butterworth":
fft_values = np.abs(np.fft.fft(self.app_data.data))
fft_freq = np.zeros(len(fft_values))
for i in range(len(fft_freq)):
fft_freq[i] = i / (len(fft_freq) *
self.app_data.filter.Ts)
return np.array([fft_freq, fft_values])
else:
return np.abs(np.fft.fft(self.app_data.data))
else:
raise ValueError("Error: Must import data first.")
elif plot_type == "Filter Response":
if self.app_data.filter_applied:
if self.app_data.filter_type == "Butterworth":
sos = np.zeros([len(self.app_data.filter.IIR_filters), 6])
idx = 0
for filter in self.app_data.filter.IIR_filters:
if filter.P_order == 2:
sos[idx] = [
filter.P_coeff[0], filter.P_coeff[1],
filter.P_coeff[2], 1, filter.Q_coeff[0],
filter.Q_coeff[1]
]
idx += 1
elif filter.P_order == 1:
sos[idx] = [
0, filter.P_coeff[0], filter.P_coeff[1], 1,
filter.Q_coeff[0], 0
]
idx += 1
w, h = sc.sosfreqz(sos, worN=None, whole=False)
w = w / (2 * np.pi * self.app_data.filter.Ts)
return np.array([w, np.abs(h)])
elif self.app_data.filter_type == "IIR Filter":
b = self.app_data.filter.P_coeff
a = np.concatenate([[1], self.app_data.filter.Q_coeff])
w, h = sc.freqz(b=b, a=a)
return np.array([w, np.abs(h)])
elif self.app_data.filter_type == "FIR Filter":
w, h = sc.freqz(b=self.app_data.filter.filter_coeffs)
w = w / (2 * np.pi * self.app_data.filter.Ts)
return np.array([w, np.abs(h)])
else:
raise ValueError("Must apply a filter first.")
def test_spatial_filter(lats_grid):
"""Test creation and frequency response of a latitude-dependent filter."""
f = lats_grid * 0.1
filt = filtering.filter.SpatialFilter(f.flatten(), 1)
for freq, filter_obj in zip(f, filt._filter):
w, h = signal.sosfreqz(filter_obj)
assert np.all(abs(h)[w < freq] < 0.1)
def plot_response(name, sos_real, sos_imag):
_, h_real = signal.sosfreqz(sos_real, whole=True)
w, h_imag = signal.sosfreqz(sos_imag, whole=True)
h = h_real / h_imag
# h = h_imag
fig, ax1 = pyplot.subplots()
ax1.set_title(f"Frequency response ({name})")
ax1.plot(w, abs(h), "b", alpha=0.2)
ax1.set_ylabel("Amplitude", color="b")
ax1.set_xlabel("Frequency [rad/sample]")
ax2 = ax1.twinx()
angles = numpy.unwrap(numpy.angle(h))
ax2.plot(w, angles, "g")
ax2.set_ylabel("Angle (radians)", color="g")
ax2.grid()
ax2.axis("tight")
def bandpass_filter(data,
lowcut,
highcut,
sampling_frequency,
order=5,
plot_on=0):
"""
Bandpass filter signal between locut and highcut frequencies
Uses butterworth second order section.
Wrapper for scipy.signal.butter
Adapted from: https://stackoverflow.com/a/48677312/1886357
Inputs:
data (1d numpy array)
lowcut: low cutoff frequency
highcut: high cutoff frequency
sampling_frequency: frequency (Hz) at which data was sampled
order: order of filter (higher is sharper corners) (5)
plot_on (int): 0 no plot, 1 to plot filter, original, and filtered signals
Outputs:
data_filtered (1d numpy array) -- same size as data, but filtered
butter_sos: butterworth bandpass filter (second order section)
"""
nyq = 0.5 * sampling_frequency
low = lowcut / nyq
high = highcut / nyq
butter_sos = signal.butter(order, [low, high],
analog=False,
btype='band',
output='sos')
filtered_data = signal.sosfiltfilt(butter_sos, data)
if plot_on:
print("Plotting")
# Filter
w, h = signal.sosfreqz(butter_sos, worN=2000)
plt.subplot(2, 1, 1)
plt.plot((sampling_frequency * 0.5 / np.pi) * w, abs(h))
plt.axvline(lowcut, color='r', linewidth=0.5)
plt.axvline(highcut, color='r', linewidth=0.5)
plt.ylabel('Gain')
plt.xlabel('Frequency')
plt.autoscale(enable=True, axis='x', tight=True)
# Data: original and filtered
plt.subplot(2, 1, 2)
plt.plot(data, color=(0.7, 0.7, 0.7), linewidth=0.5)
plt.plot(filtered_data, color='r', linewidth=1)
plt.xlabel('Sample')
plt.ylabel('Value')
plt.autoscale(enable=True, axis='x', tight=True)
plt.tight_layout()
return filtered_data, butter_sos
def comp_dac_resp(dpe_fb,
sim_len,
rrc_beta,
PAPR=9,
prms_dac=(16e9, 2, 'sos', 6),
os=2):
"""
Compensate frequency response of a simulated digital-to-analog converter(DAC).
Parameters
----------
dpe_fb : int
symbol rate to compensate for
sim_len : int
length of the oversampled signal array
rrc_beta : float
root-raised cosine roll-off factor of the simulated signal
PAPR: int (optional)
peak to average power ratio of the signal
prms_dac: tuple(float, int, str, int)
DAC filer parameters for calculating the filter response using scipy.signal
os: int (optional)
oversampling factor of the signal
"""
dpe_fs = dpe_fb * os
# Derive RRC filter frequency response np.sqrt(n_f)
T_rrc = 1 / dpe_fb
fre_rrc = np.fft.fftfreq(sim_len) * dpe_fs
rrc_f = rrcos_freq(fre_rrc, rrc_beta, T_rrc)
rrc_f /= rrc_f.max()
n_f = rrc_f**2
# Derive bessel filter (DAC) frequency response d_f
cutoff, order, frmt, enob = prms_dac
system_dig = signal.bessel(order,
cutoff,
'low',
analog=False,
output=frmt,
norm='mag',
fs=dpe_fs)
# w_bes=np.linspace(0,fs-fs/worN,worN)
w_bes, d_f = signal.sosfreqz(system_dig,
worN=sim_len,
whole=True,
fs=dpe_fs)
# Calculate dpe filter p_f
df = dpe_fs / sim_len
alpha = 10**(PAPR / 10) / (6 * dpe_fb * 2**(2 * enob)) * np.sum(
abs(d_f)**2 * n_f * df)
p_f = n_f * np.conj(d_f) / (n_f * abs(d_f)**2 + alpha)
return p_f
def third_octave(speech):
## Filtering of the time series
sampleRate = 44100.0
nyquistRate = sampleRate/2.0 # 0.5 times the sampling frequency
centerFrequency_Hz = np.array([39, 50, 63, 79, 99, 125, 157, 198, 250, 315, 397, 500, 630, 794, 1000, 1260, 1588, 2000, 2520, 3176, 4000, 5040, 6352, 8000, 10080, 12704, 16000])
G = 2 #base-2 rules
factor = np.power(G, 1.0/6.0)
lowerCutoffFrequency_Hz=centerFrequency_Hz/factor
upperCutoffFrequency_Hz=centerFrequency_Hz*factor
all_filter = []
# ##fig=plt.figure()
# ##plt.title('Speech Signal')
# ##plt.plot(speech)
# ##plt.show()
# plt.figure()
# plt.ylabel('Magnitude [dB]')
# plt.xlabel('Frequency [rad/sample]')
# plt.title('Digital filter frequency response')
# plt.grid()
# plt.axis([-0.2, 3.2, -80, 20])
for lower,upper in zip(lowerCutoffFrequency_Hz, upperCutoffFrequency_Hz):
# Design filter
sos = signal.butter( N=4, Wn=np.array([lower, upper])/nyquistRate, btype='bandpass', analog=False, output='sos');
# # Compute frequency response of the filter.
w, h = signal.sosfreqz(sos)
#
## for i in range(len(h)):
## if h[i] == 0j:
## h[i] = min(j for j in h if j > 0)
##
# plt.plot(w, 20 * np.log10(abs(h)/max(h)), 'b')
# Filter signal
filteredSpeech = signal.sosfiltfilt(sos, speech)
for i in filteredSpeech:
all_filter.append(i)
# plt.plot(all_filter)
# plt.figure()
# plt.title('Third Octave-band Filtered Speech')
# plt.plot(filteredSpeech)
# new = np.round(all_filter).astype('int16')
# new_sound = sound._spawn(new)
# new_sound.export("music/clicks.mp3", format="mp3")
# print(all_filter)
return all_filter
def compute_frequency_response(filter_coefs, a_vals, fs):
"""Compute the frequency response of a filter.
Parameters
----------
filter_coefs : 1d or 2d array
If 1d, interpreted as the B-value filter coefficients.
If 2d, interpreted as the second-order (sos) filter coefficients.
a_vals : 1d array or None
The A-value filter coefficients for a filter.
If second-order filter coefficients are provided in `filter_coefs`, must be None.
fs : float
Sampling rate, in Hz.
Returns
-------
f_db : 1d array
Frequency vector corresponding to attenuation decibels, in Hz.
db : 1d array
Degree of attenuation for each frequency specified in `f_db`, in dB.
Examples
--------
Compute the frequency response for an FIR filter:
>>> from neurodsp.filt.fir import design_fir_filter
>>> filter_coefs = design_fir_filter(fs=500, pass_type='bandpass', f_range=(8, 12))
>>> f_db, db = compute_frequency_response(filter_coefs, 1, fs=500)
Compute the frequency response for an IIR filter, which uses SOS coefficients:
>>> from neurodsp.filt.iir import design_iir_filter
>>> sos_coefs = design_iir_filter(fs=500, pass_type='bandpass',
... f_range=(8, 12), butterworth_order=3)
>>> f_db, db = compute_frequency_response(sos_coefs, None, fs=500)
"""
if filter_coefs.ndim == 1 and a_vals is not None:
# Compute response for B & A value filter coefficient inputs
w_vals, h_vals = freqz(filter_coefs, a_vals, worN=int(fs * 2))
elif filter_coefs.ndim == 2 and a_vals is None:
# Compute response for sos filter coefficient inputs
w_vals, h_vals = sosfreqz(filter_coefs, worN=int(fs * 2))
else:
raise ValueError(
"The organization of the filter coefficient inputs is not understood."
)
f_db = w_vals * fs / (2. * np.pi)
db = 20 * np.log10(abs(h_vals))
return f_db, db
def response(self, freqs=None, num_points=1024):
if freqs is not None:
freqs = np.array(freqs)
w = 2 * np.pi * freqs / self.sample_rate
else:
w = num_points
w2, h = signal.sosfreqz(self.sos, w)
return data.Spectrum(h,
self.sample_rate,
freqs=(self.sample_rate * w2 / (2 * np.pi)))
def designFilters(freqDict, fs=48000, plot=False):
"""
Design octave band filters
:param freqDict: filter specification dict
:param fs: sample rate
:param plot: bool if filters should be plotted
:return: filter coefficients
"""
freqs = freqDict["f"]
b = freqDict["b"]
G = freqDict["G"]
order = 4
filters = np.empty((0, 6))
for index in range(np.size(freqs, axis=0)):
lowCutoff = 2 * freqs[index, 0] / fs
highCutoff = 2 * freqs[index, 2] / fs
sos = signal.butter(order, [lowCutoff, highCutoff],
btype="bandpass",
output="sos")
filters = np.append(filters, sos, axis=0)
if plot is True:
# Requirements
maskLevelmax = -np.array(
[0.15, 0.2, 0.4, 1.1, 4.5, 4.5, 200, 200, 200, 200])
maskLevelmin = -np.array(
[-0.15, -0.15, -0.15, -0.15, -0.15, 2.3, 18, 42.5, 62, 75])
breakpoints = np.array(
[0, 1 / 8, 1 / 4, 3 / 8, 1 / 2, 1 / 2, 1, 2, 3, 4])
freqH = 1 + ((G**(1 / (2 * b)) - 1) /
(G**(1 / 2) - 1)) * (G**(breakpoints) - 1)
freqL = 1 / freqH
plt.figure("Filter responses with {} bands from {} Hz to {} Hz".format(
np.size(freqs, 0), np.int(freqs[0, 0]), np.int(freqs[-1, 2])))
for index in range(np.size(freqs, axis=0)):
# Plot
w, h = signal.sosfreqz(filters[(order * index):(order * index +
order), :],
worN=fs)
plt.semilogx(freqH * freqs[index, 1], maskLevelmax, "k--")
plt.semilogx(freqH * freqs[index, 1], maskLevelmin, "k--")
plt.semilogx(freqL * freqs[index, 1], maskLevelmax, "k--")
plt.semilogx(freqL * freqs[index, 1], maskLevelmin, "k--")
plt.semilogx((fs * 0.5 / np.pi) * w, 20 * np.log10(abs(h)))
plt.ylim([-100, 1])
plt.show()
return filters
def test_freq_resp_sos(self):
# Test that frequency response meets tolerance from ITU-R BS.468-4
fs = 400000
sos = ITU_R_468_weighting(fs, output='sos')
w, h = signal.sosfreqz(sos, 2*pi*frequencies/fs)
levels = 20 * np.log10(abs(h))
if mpl:
plt.figure('468')
plt.semilogx(frequencies, levels, alpha=0.7, label='sos')
plt.legend()
assert all(np.less_equal(levels, responses + upper_limits))
assert all(np.greater_equal(levels, responses + lower_limits))
from __future__ import division, print_function
import numpy as np
from scipy.signal import butter, sosfreqz, sosfilt
import matplotlib.pyplot as plt
sos = butter(10, [0.04, 0.16],
btype="bandpass", output="sos")
w, h = sosfreqz(sos, worN=8000)
# Plot the magnitude and phase of the frequency response.
plt.figure(figsize=(4.0, 4.0))
plt.subplot(211)
plt.plot(w/np.pi, np.abs(h))
plt.grid(alpha=0.25)
plt.ylabel('Gain')
plt.subplot(212)
plt.plot(w/np.pi, np.angle(h))
yaxis = plt.gca().yaxis
yaxis.set_ticks([-np.pi, -0.5*np.pi, 0, 0.5*np.pi, np.pi])
yaxis.set_ticklabels([r'$-\pi$', r'$-\pi/2$', '0', r'$\pi/2$', r'$\pi$'])
plt.xlabel('Normalized frequency')
plt.grid(alpha=0.25)
plt.ylabel('Phase')
plt.tight_layout()
plt.savefig("sos_bandpass_response_freq.pdf")
# Plot the step response.
x = np.ones(200)
y = sosfilt(sos, x)
# Sample rate and desired cutoff frequencies (in Hz).
fs = 4800.0
lowcut = 400.0
highcut = 1200.0
# Plot the frequency response for a few different orders.
plt.figure(figsize=(4.0, 4.0))
# First plot the desired ideal response as a green(ish) rectangle.
rect = plt.Rectangle((lowcut, 0), highcut - lowcut, 1.0,
facecolor="#60ff60",
edgecolor='k',
alpha=0.15)
plt.gca().add_patch(rect)
for order in [3, 6, 12]:
sos = butter_bandpass(lowcut, highcut, fs, order)
w, h = sosfreqz(sos, worN=2000)
plt.plot((fs*0.5/np.pi)*w, abs(h), 'k',
alpha=(order+1)/13, label="order = %d" % order)
plt.plot([0, 0.5 * fs], [np.sqrt(0.5), np.sqrt(0.5)],
'k--', alpha=0.6, linewidth=1, label=r'$\sqrt{2}/2$')
plt.xlim(0, 0.5*fs)
plt.xlabel('Frequency (Hz)')
plt.ylabel('Gain')
plt.grid(alpha=0.5)
plt.legend(framealpha=1, shadow=True, loc='best')
plt.title("Amplitude response for\nButterworth bandpass filters", fontsize=10)
plt.text(430, 0.07, "lowcut: %4g Hz\nhighcut: %4g Hz" % (lowcut, highcut),
fontsize=8)
plt.tight_layout()
plt.savefig("bandpass_example_response.pdf")
