def test_butterBandpass_egde(self):
# no signal allowed
b, a = self.util.butterBandpass(5, 5, 16)
_, h = freqz(b, a, worN=32)
self.assertEquals(np.count_nonzero(abs(h)), 0)
# everything gets through (except 0)
b, a = self.util.butterBandpass(0, 8, 16)
_, h = freqz(b, a, worN=16)
self.assertAlmostEqual(sum(abs(h)), len(h)-1, delta = 1)
b, a = self.util.butterBandpass(0.5, 8, 16)
_, h = freqz(b, a, worN=16)
self.assertAlmostEqual(sum(abs(h)), len(h)-1, delta = 1)
b, a = self.util.butterBandpass(-1, 9, 16)
_, h = freqz(b, a, worN=16)
self.assertAlmostEqual(sum(abs(h)), len(h)-1, delta = 1)
def test_butterBandpass_egde(self):
# no signal allowed
b, a = self.util.butterBandpass(5, 5, 16)
_, h = freqz(b, a, worN=32)
self.assertEquals(np.count_nonzero(abs(h)), 0)
# everything gets through (except 0)
b, a = self.util.butterBandpass(0, 8, 16)
_, h = freqz(b, a, worN=16)
self.assertAlmostEqual(sum(abs(h)), len(h)-1, delta = 1)
b, a = self.util.butterBandpass(0.5, 8, 16)
_, h = freqz(b, a, worN=16)
self.assertAlmostEqual(sum(abs(h)), len(h)-1, delta = 1)
b, a = self.util.butterBandpass(-1, 9, 16)
_, h = freqz(b, a, worN=16)
self.assertAlmostEqual(sum(abs(h)), len(h)-1, delta = 1)
def test_butterBandpass(self):
samplingRate = 32
i = samplingRate / 4
b, a = self.util.butterBandpass(i-1, i+1, samplingRate)
_, h = freqz(b, a, worN=samplingRate*4)
h = abs(h)
self.assertEqual(np.argmax(h), len(h)/2)
self.assertAlmostEqual(max(h), 1, delta=0.1)
self.assertAlmostEqual(h[0], 0, delta=0.01)
self.assertAlmostEqual(h[len(h)-1], 0, delta=0.01)
def test_butterBandpass(self):
samplingRate = 32
i = samplingRate / 4
b, a = self.util.butterBandpass(i-1, i+1, samplingRate)
_, h = freqz(b, a, worN=samplingRate*4)
h = abs(h)
self.assertEqual(np.argmax(h), len(h)/2)
self.assertAlmostEqual(max(h), 1, delta=0.1)
self.assertAlmostEqual(h[0], 0, delta=0.01)
self.assertAlmostEqual(h[len(h)-1], 0, delta=0.01)
def plot_frequency_response(self,
filter_coeffs,
framerate,
cutoffs,
title=None):
'''
Plot response to a low/high/bandpass filter.
Filter coefficients from from calling iirfilter().
If that function was called such that it returned
nominator/denominator of the transfer function, namely
a and b, hen filter_coeffs should be a tuple (a,b)
if the function was called requesting second order segments,
(sos), then filter_coeffs should be the sos.
@param filter_coeffs: definiting filter characteristics
@type filter_coeffs: {(np_arr, np_arr) | np_arr}
@param framerate: sample frequency of the audio file.
@type int
@param cutoffs: frequencies (Hz) at which filter is supposed to cut off
@type cutoffs: {int | [int]}
@param title: optional title of the figure. If None,
a title is created from the cutoff freqs.
@type str
'''
if type(cutoffs) != list:
cutoffs = [cutoffs]
if type(filter_coeffs) == tuple:
(a, b) = filter_coeffs
w, h = freqz(b, a, worN=8000)
else:
w, h = sosfreqz(filter_coeffs, worN=8000)
fig = plt.figure()
ax = fig.add_subplot(1, 1, 1)
ax.plot(0.5 * framerate * w / np.pi, np.abs(h), 'b') # Blue
ax.plot(cutoffs[0], 0.5 * np.sqrt(2), 'ko')
ax.axvline(cutoffs[0], color='k')
if len(cutoffs) > 1:
ax.plot(cutoffs[1], 0.5 * np.sqrt(2), 'ko')
ax.axvline(cutoffs[1], color='k')
# Since x axis will be log, cannot start
# x vals at 0. To make best use of the
# horizontal space, start plotting at
# 5Hz below the low cutoff freq:
ax.set_xlim(cutoffs[0] - 5,
max(cutoffs) + max(cutoffs)) #0.5*framerate)
ax.set_xscale('log')
ax.set_yscale('log')
if title is not None:
fig.suptitle(title)
else:
fig.suptitle(f"Filter Frequency Response cutoff(s): {cutoffs} Hz")
ax.set_xlabel('Log frequency [Hz]')
ax.grid()
fig.show()
def plot_filter_responce(filter_coefficients):
w, h = freqz(filter_coefficients)
fig = plt.figure()
plt.title('Digital filter frequency 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')
plt.show()
def test_cheby2_low_pass_filter():
rate = 16000 # sampling rate of speech waveform(Hz)
cut_off = 700 # cut off frequency (Hz)
ripple = 0.5 # pass band maximum loss (gpass)
attenuation = 60 # stop band min attenuation (gstop)
b, a = cheby2_low_pass_coefficients(cut_off, rate, ripple, attenuation)
# Plot the frequency response.
w, h = fd.freqz(b, a, worN=8000)
plt.subplot(2, 1, 1)
plt.plot(0.5 * rate * w / np.pi, np.abs(h), 'b')
plt.plot(cut_off, 0.5 * np.sqrt(2), 'ko')
plt.axvline(cut_off, color='k')
plt.xlim(0, 0.5 * rate)
plt.title("Low pass 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 * rate) # 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.
data = np.sin(1.2 * 2 * np.pi * t) + 1.5 * np.cos(
9 * 2 * np.pi * t) + 0.5 * np.sin(12.0 * 2 * np.pi * t)
# Filter the data, and plot both the original and filtered signals.
y = cheby2_low_pass_filter(data, cut_off, rate, ripple, attenuation)
plt.subplot(2, 1, 2)
plt.plot(t, data, 'b-', label='data')
plt.plot(t, y, 'g-', linewidth=2, label='filtered data')
plt.xlabel('Time [sec]')
plt.grid()
plt.legend()
plt.subplots_adjust(hspace=0.35)
plt.show()
# TODO
pass