def mix_cosines():
"""Plots three periods of a mix of cosines.
"""
# create a SumSignal
cos_sig = thinkdsp.CosSignal(freq=440, amp=1.0, offset=0)
sin_sig = thinkdsp.SinSignal(freq=880, amp=0.5, offset=0)
mix = sin_sig + cos_sig
# create a wave
wave = mix.make_wave(duration=0.5, start=0, framerate=11025)
print('Number of samples', len(wave.ys))
print('Timestep in ms', 1.0 / 11025 * 1000)
# select a segment
period = mix.period
segment = wave.segment(start=0, duration=period*3)
# plot the segment
thinkplot.preplot(1)
segment.plot()
thinkplot.Save(root='sounds4',
xlabel='Time (s)',
axis=[0, period*3, -1.55, 1.55],
formats=FORMATS,
legend=False)
def plot_filters(close):
"""Plots the filter that corresponds to diff, deriv, and integral.
"""
thinkplot.preplot(3, cols=2)
diff_window = np.array([1.0, -1.0])
diff_filter = make_filter(diff_window, close)
diff_filter.plot(label='diff')
deriv_filter = close.make_spectrum()
deriv_filter.hs = PI2 * 1j * deriv_filter.fs
deriv_filter.plot(label='derivative')
thinkplot.config(xlabel='Frequency (1/day)',
ylabel='Amplitude ratio',
loc='upper left')
thinkplot.subplot(2)
integ_filter = deriv_filter.copy()
integ_filter.hs = 1 / (PI2 * 1j * integ_filter.fs)
integ_filter.plot(label='integral')
thinkplot.config(xlabel='Frequency (1/day)',
ylabel='Amplitude ratio',
yscale='log')
thinkplot.save('diff_int3')
def three_spectrums():
"""Makes a plot showing three spectrums for a sinusoid.
"""
thinkplot.preplot(rows=1, cols=3)
pyplot.subplots_adjust(wspace=0.3,
hspace=0.4,
right=0.95,
left=0.1,
top=0.95,
bottom=0.05)
xticks = range(0, 900, 200)
thinkplot.subplot(1)
thinkplot.config(xticks=xticks)
discontinuity(num_periods=30, hamming=False)
thinkplot.subplot(2)
thinkplot.config(xticks=xticks)
discontinuity(num_periods=30.25, hamming=False)
thinkplot.subplot(3)
thinkplot.config(xticks=xticks)
discontinuity(num_periods=30.25, hamming=True)
thinkplot.save(root='windowing1')
def triangle_example(freq):
"""Makes a figure showing a triangle wave.
freq: frequency in Hz
"""
framerate = 10000
signal = thinkdsp.TriangleSignal(freq)
duration = signal.period * 3
segment = signal.make_wave(duration, framerate=framerate)
segment.plot()
thinkplot.save(root='triangle-%d-1' % freq,
xlabel='Time (s)',
axis=[0, duration, -1.05, 1.05])
wave = signal.make_wave(duration=0.5, framerate=framerate)
spectrum = wave.make_spectrum()
thinkplot.preplot(cols=2)
spectrum.plot()
thinkplot.config(xlabel='Frequency (Hz)', ylabel='Amplitude')
thinkplot.subplot(2)
spectrum.plot()
thinkplot.config(ylim=[0, 500], xlabel='Frequency (Hz)')
thinkplot.save(root='triangle-%d-2' % freq)
def main():
# make_figures()
wave = thinkdsp.read_wave('28042__bcjordan__voicedownbew.wav')
wave.unbias()
wave.normalize()
track_pitch(wave)
return
thinkplot.preplot(rows=1, cols=2)
plot_shifted(wave, 0.0003)
thinkplot.config(xlabel='time (s)',
ylabel='amplitude',
ylim=[-1, 1])
thinkplot.subplot(2)
plot_shifted(wave, 0.00225)
thinkplot.config(xlabel='time (s)',
ylim=[-1, 1])
thinkplot.save(root='autocorr3')
def plot_sines():
"""Makes figures showing correlation of sine waves with offsets.
"""
wave1 = make_wave(0)
wave2 = make_wave(offset=1)
thinkplot.preplot(2)
wave1.segment(duration=0.01).plot(label='wave1')
wave2.segment(duration=0.01).plot(label='wave2')
corr_matrix = numpy.corrcoef(wave1.ys, wave2.ys, ddof=0)
print(corr_matrix)
thinkplot.save(root='autocorr1',
xlabel='time (s)',
ylabel='amplitude',
ylim=[-1.05, 1.05])
offsets = numpy.linspace(0, PI2, 101)
corrs = []
for offset in offsets:
wave2 = make_wave(offset)
corr = corrcoef(wave1.ys, wave2.ys)
corrs.append(corr)
thinkplot.plot(offsets, corrs)
thinkplot.save(root='autocorr2',
xlabel='offset (radians)',
ylabel='correlation',
xlim=[0, PI2],
ylim=[-1.05, 1.05])
def chirp_spectrum():
"""Plots the spectrum of a one-second one-octave linear chirp.
"""
signal = thinkdsp.Chirp(start=220, end=440)
wave = signal.make_wave(duration=1)
thinkplot.preplot(3, cols=3)
duration = 0.01
wave.segment(0, duration).plot()
thinkplot.config(ylim=[-1.05, 1.05])
thinkplot.subplot(2)
wave.segment(0.5, duration).plot()
thinkplot.config(yticklabels='invisible',
xlabel='Time (s)')
thinkplot.subplot(3)
wave.segment(0.9, duration).plot()
thinkplot.config(yticklabels='invisible')
thinkplot.save('chirp3')
spectrum = wave.make_spectrum()
spectrum.plot(high=700)
thinkplot.save('chirp1',
xlabel='Frequency (Hz)')
def chirp_spectrum():
"""Plots the spectrum of a one-second one-octave linear chirp.
"""
signal = thinkdsp.Chirp(start=220, end=440)
wave = signal.make_wave(duration=1)
thinkplot.preplot(3, cols=3)
duration = 0.01
wave.segment(0, duration).plot()
thinkplot.config(ylim=[-1.05, 1.05])
thinkplot.subplot(2)
wave.segment(0.5, duration).plot()
thinkplot.config(yticklabels='invisible',
xlabel='Time (s)')
thinkplot.subplot(3)
wave.segment(0.9, duration).plot()
thinkplot.config(yticklabels='invisible')
thinkplot.save('chirp3')
spectrum = wave.make_spectrum()
spectrum.plot(high=700)
thinkplot.save('chirp1',
xlabel='Frequency (Hz)',
ylabel='Amplitude')
def window_plot():
"""Makes a plot showing a sinusoid, hamming window, and their product.
"""
signal = thinkdsp.SinSignal(freq=440)
duration = signal.period * 10.25
wave1 = signal.make_wave(duration)
wave2 = signal.make_wave(duration)
ys = np.hamming(len(wave1.ys))
ts = wave1.ts
window = thinkdsp.Wave(ys, ts, wave1.framerate)
wave2.hamming()
thinkplot.preplot(rows=3, cols=1)
pyplot.subplots_adjust(wspace=0.3, hspace=0.3,
right=0.95, left=0.1,
top=0.95, bottom=0.05)
thinkplot.subplot(1)
wave1.plot()
thinkplot.config(axis=[0, duration, -1.07, 1.07])
thinkplot.subplot(2)
window.plot()
thinkplot.config(axis=[0, duration, -1.07, 1.07])
thinkplot.subplot(3)
wave2.plot()
thinkplot.config(axis=[0, duration, -1.07, 1.07],
xlabel='Time (s)')
thinkplot.save(root='windowing2')
def window_plot():
"""Makes a plot showing a sinusoid, hamming window, and their product.
"""
signal = thinkdsp.SinSignal(freq=440)
duration = signal.period * 10.25
wave1 = signal.make_wave(duration)
wave2 = signal.make_wave(duration)
ys = numpy.hamming(len(wave1.ys))
window = thinkdsp.Wave(ys, wave1.framerate)
wave2.hamming()
thinkplot.preplot(rows=3, cols=1)
pyplot.subplots_adjust(wspace=0.3,
hspace=0.3,
right=0.95,
left=0.1,
top=0.95,
bottom=0.05)
thinkplot.subplot(1)
wave1.plot()
thinkplot.config(axis=[0, duration, -1.07, 1.07])
thinkplot.subplot(2)
window.plot()
thinkplot.config(axis=[0, duration, -1.07, 1.07])
thinkplot.subplot(3)
wave2.plot()
thinkplot.config(axis=[0, duration, -1.07, 1.07], xlabel='time (s)')
thinkplot.save(root='windowing2')
def segment_violin(start=1.2, duration=0.6):
"""Load a violin recording and plot its spectrum.
start: start time of the segment in seconds
duration: in seconds
"""
wave = thinkdsp.read_wave('92002__jcveliz__violin-origional.wav')
# extract a segment
segment = wave.segment(start, duration)
segment.normalize()
# plot the spectrum
spectrum = segment.make_spectrum()
thinkplot.preplot(1)
spectrum.plot(high=10000)
thinkplot.Save(root='sounds3',
xlabel='Frequency (Hz)',
ylabel='Amplitude',
formats=FORMATS,
legend=False)
# print the top 5 peaks
peaks = spectrum.peaks()
for amp, freq in peaks[:10]:
print(freq, amp)
def plot_sincs():
start = 1.0
duration = 0.01
factor = 4
short = wave.segment(start=start, duration=duration)
short.plot()
sampled = sample(short, factor)
sampled.plot_vlines(color='gray')
spectrum = sampled.make_spectrum()
boxcar = make_boxcar(spectrum, factor)
sinc = boxcar.make_wave()
sinc.shift(sampled.ts[0])
sinc.roll(len(sinc) // 2)
thinkplot.preplot(1)
sinc.plot()
# CAUTION: don't call plot_sinc_demo with a large wave or it will
# fill memory and crash
plot_sinc_demo(short, 4)
start = short.start + 0.004
duration = 0.00061
plot_sinc_demo(short, 4, start, duration)
thinkplot.config(xlim=[start, start + duration],
ylim=[-0.05, 0.17],
legend=False)
def segment_violin(start=1.2, duration=0.6):
"""Load a violin recording and plot its spectrum.
start: start time of the segment in seconds
duration: in seconds
"""
wave = thinkdsp.read_wave('92002__jcveliz__violin-origional.wav')
# extract a segment
segment = wave.segment(start, duration)
segment.normalize()
# plot the spectrum
spectrum = segment.make_spectrum()
thinkplot.preplot(1)
spectrum.plot(high=10000)
thinkplot.Save(root='sounds3',
xlabel='Frequency (Hz)',
ylabel='Amplitude',
formats=FORMATS,
legend=False)
# print the top 5 peaks
peaks = spectrum.peaks()
for amp, freq in peaks[:10]:
print(freq, amp)
assert abs(peaks[0][0] - 3762.382899) < 1e-7
def plot_beeps():
wave = thinkdsp.read_wave('253887__themusicalnomad__positive-beeps.wav')
wave.normalize()
thinkplot.preplot(3)
# top left
ax1 = plt.subplot2grid((4, 2), (0, 0), rowspan=2)
plt.setp(ax1.get_xticklabels(), visible=False)
wave.plot()
thinkplot.config(title='Input waves', legend=False)
# bottom left
imp_sig = thinkdsp.Impulses([0.01, 0.4, 0.8, 1.2],
amps=[1, 0.5, 0.25, 0.1])
impulses = imp_sig.make_wave(start=0,
duration=1.3,
framerate=wave.framerate)
ax2 = plt.subplot2grid((4, 2), (2, 0), rowspan=2, sharex=ax1)
impulses.plot()
thinkplot.config(xlabel='Time (s)')
# center right
convolved = wave.convolve(impulses)
ax3 = plt.subplot2grid((4, 2), (1, 1), rowspan=2)
plt.title('Convolution')
convolved.plot()
thinkplot.config(xlabel='Time (s)')
thinkplot.save(root='sampling1', formats=FORMATS, legend=False)
def mix_cosines():
"""Plots three periods of a mix of cosines.
"""
# create a SumSignal
cos_sig = thinkdsp.CosSignal(freq=440, amp=1.0, offset=0)
sin_sig = thinkdsp.SinSignal(freq=880, amp=0.5, offset=0)
mix = sin_sig + cos_sig
# create a wave
wave = mix.make_wave(duration=1.0, start=0, framerate=11025)
print('Number of samples', len(wave))
print('Timestep in ms', 1000 / wave.framerate)
assert len(wave) == wave.framerate
# select a segment
period = mix.period
segment = wave.segment(start=0, duration=period * 3)
# plot the segment
thinkplot.preplot(1)
segment.plot()
thinkplot.Save(root='sounds4',
xlabel='Time (s)',
axis=[0, period * 3, -1.55, 1.55],
formats=FORMATS,
legend=False)
def main():
p1 = Hockey()
p2 = Hockey()
thinkplot.Clf()
thinkplot.Pmf(p1)
thinkplot.Pmf(p2)
thinkplot.Save(root='hockey_self4_prior',
xlabel='',
ylabel='Probability',
formats=['pdf'])
p1.UpdateSet([0, 2, 8, 4])
p2.UpdateSet([1, 3, 1, 0])
# p2.UpdateSet([1,3,1,0,1,2,3,4,1,2,2,3,1,2,4,1,3,2,1,1,2,2,1,3,3,1,1,2,4,1,2,1,2,1,4,2,3,1,1])
thinkplot.Clf()
thinkplot.preplot(num=2)
thinkplot.Pmf(p1)
thinkplot.Pmf(p2)
thinkplot.Save(root='hockey_self4_posterior',
xlabel='',
ylabel='Probability',
formats=['pdf'])
p1 = MakeGoalPmf(p1)
p2 = MakeGoalPmf(p2)
thinkplot.Clf()
thinkplot.preplot(num=2)
thinkplot.Pmf(p1)
thinkplot.Pmf(p2)
thinkplot.Save(root='hockey_self4_MakeGoalPmf',
xlabel='',
ylabel='Probability',
formats=['pdf'])
def plot_response():
thinkplot.preplot(cols=2)
response = thinkdsp.read_wave('180961__kleeb__gunshots.wav')
response = response.segment(start=0.26, duration=5.0)
response.normalize()
response.plot()
thinkplot.config(xlabel='time',
xlim=[0, 5.0],
ylabel='amplitude',
ylim=[-1.05, 1.05])
thinkplot.subplot(2)
transfer = response.make_spectrum()
transfer.plot()
thinkplot.config(xlabel='frequency', xlim=[0, 22500], ylabel='amplitude')
thinkplot.save(root='systems6')
wave = thinkdsp.read_wave('92002__jcveliz__violin-origional.wav')
wave.ys = wave.ys[:len(response)]
wave.normalize()
spectrum = wave.make_spectrum()
output = (spectrum * transfer).make_wave()
output.normalize()
wave.plot(color='0.7')
output.plot(alpha=0.4)
thinkplot.config(xlabel='time',
xlim=[0, 5.0],
ylabel='amplitude',
ylim=[-1.05, 1.05])
thinkplot.save(root='systems7')
def make_figures():
wave1 = make_wave(0)
wave2 = make_wave(offset=1)
thinkplot.preplot(2)
wave1.segment(duration=0.01).plot(label='wave1')
wave2.segment(duration=0.01).plot(label='wave2')
numpy.corrcoef(wave1.ys, wave2.ys)
thinkplot.save(root='autocorr1',
xlabel='time (s)',
ylabel='amplitude')
offsets = numpy.linspace(0, PI2, 101)
corrs = []
for offset in offsets:
wave2 = make_wave(offset)
corr = numpy.corrcoef(wave1.ys, wave2.ys)[0, 1]
corrs.append(corr)
thinkplot.plot(offsets, corrs)
thinkplot.save(root='autocorr2',
xlabel='offset (radians)',
ylabel='correlation',
xlim=[0, PI2])
def aliasing_example(offset=0.000003):
"""Makes a figure showing the effect of aliasing.
"""
framerate = 10000
thinkplot.preplot(num=2)
freq1 = 4500
signal = thinkdsp.CosSignal(freq1)
duration = signal.period*5
segment = signal.make_wave(duration, framerate=framerate)
thinkplot.Hlines(0, 0, duration, color='gray')
segment.shift(-offset)
segment.plot_vlines(label=freq1, linewidth=3)
freq2 = 5500
signal = thinkdsp.CosSignal(freq2)
segment = signal.make_wave(duration, framerate=framerate)
segment.shift(+offset)
segment.plot_vlines(label=freq2, linewidth=3)
thinkplot.save(root='aliasing1',
xlabel='Time (s)',
axis=[-0.00002, duration, -1.05, 1.05]
)
def plot_sines():
"""Makes figures showing correlation of sine waves with offsets.
"""
wave1 = make_wave(0)
wave2 = make_wave(offset=1)
thinkplot.preplot(2)
wave1.segment(duration=0.01).plot(label='wave1')
wave2.segment(duration=0.01).plot(label='wave2')
corr_matrix = numpy.corrcoef(wave1.ys, wave2.ys, ddof=0)
print(corr_matrix)
thinkplot.save(root='autocorr1',
xlabel='time (s)',
ylabel='amplitude',
ylim=[-1.05, 1.05])
offsets = numpy.linspace(0, PI2, 101)
corrs = []
for offset in offsets:
wave2 = make_wave(offset)
corr = corrcoef(wave1.ys, wave2.ys)
corrs.append(corr)
thinkplot.plot(offsets, corrs)
thinkplot.save(root='autocorr2',
xlabel='offset (radians)',
ylabel='correlation',
xlim=[0, PI2],
ylim=[-1.05, 1.05])
def plot_derivative(wave, wave2):
# compute the derivative by spectral decomposition
spectrum = wave.make_spectrum()
spectrum3 = wave.make_spectrum()
spectrum3.differentiate()
# plot the derivative computed by diff and differentiate
wave3 = spectrum3.make_wave()
wave2.plot(color="0.7", label="diff")
wave3.plot(label="derivative")
thinkplot.config(xlabel="days", xlim=[0, 1650], ylabel="dollars", loc="upper left")
thinkplot.save(root="systems4")
# plot the amplitude ratio compared to the diff filter
amps = spectrum.amps
amps3 = spectrum3.amps
ratio3 = amps3 / amps
thinkplot.preplot(1)
thinkplot.plot(ratio3, label="ratio")
window = numpy.array([1.0, -1.0])
padded = zero_pad(window, len(wave))
fft_window = numpy.fft.rfft(padded)
thinkplot.plot(abs(fft_window), color="0.7", label="filter")
thinkplot.config(
xlabel="frequency (1/days)", xlim=[0, 1650 / 2], ylabel="amplitude ratio", ylim=[0, 4], loc="upper left"
)
thinkplot.save(root="systems5")
def plot_sincs():
start = 1.0
duration = 0.01
factor = 4
short = wave.segment(start=start, duration=duration)
short.plot()
sampled = sample(short, factor)
sampled.plot_vlines(color='gray')
spectrum = sampled.make_spectrum()
boxcar = make_boxcar(spectrum, factor)
sinc = boxcar.make_wave()
sinc.shift(sampled.ts[0])
sinc.roll(len(sinc)//2)
thinkplot.preplot(1)
sinc.plot()
# CAUTION: don't call plot_sinc_demo with a large wave or it will
# fill memory and crash
plot_sinc_demo(short, 4)
start = short.start + 0.004
duration = 0.00061
plot_sinc_demo(short, 4, start, duration)
thinkplot.config(xlim=[start, start+duration],
ylim=[-0.05, 0.17], legend=False)
def plot_response():
thinkplot.preplot(cols=2)
response = thinkdsp.read_wave("180961__kleeb__gunshots.wav")
response = response.segment(start=0.26, duration=5.0)
response.normalize()
response.plot()
thinkplot.config(xlabel="time", xlim=[0, 5.0], ylabel="amplitude", ylim=[-1.05, 1.05])
thinkplot.subplot(2)
transfer = response.make_spectrum()
transfer.plot()
thinkplot.config(xlabel="frequency", xlim=[0, 22500], ylabel="amplitude")
thinkplot.save(root="systems6")
wave = thinkdsp.read_wave("92002__jcveliz__violin-origional.wav")
wave.ys = wave.ys[: len(response)]
wave.normalize()
spectrum = wave.make_spectrum()
output = (spectrum * transfer).make_wave()
output.normalize()
wave.plot(color="0.7")
output.plot(alpha=0.4)
thinkplot.config(xlabel="time", xlim=[0, 5.0], ylabel="amplitude", ylim=[-1.05, 1.05])
thinkplot.save(root="systems7")
def plot_beeps():
wave = thinkdsp.read_wave('253887__themusicalnomad__positive-beeps.wav')
wave.normalize()
thinkplot.preplot(3)
# top left
ax1 = plt.subplot2grid((4, 2), (0, 0), rowspan=2)
plt.setp(ax1.get_xticklabels(), visible=False)
wave.plot()
thinkplot.config(title='Input waves', legend=False)
# bottom left
imp_sig = thinkdsp.Impulses([0.01, 0.4, 0.8, 1.2],
amps=[1, 0.5, 0.25, 0.1])
impulses = imp_sig.make_wave(start=0, duration=1.3,
framerate=wave.framerate)
ax2 = plt.subplot2grid((4, 2), (2, 0), rowspan=2, sharex=ax1)
impulses.plot()
thinkplot.config(xlabel='Time (s)')
# center right
convolved = wave.convolve(impulses)
ax3 = plt.subplot2grid((4, 2), (1, 1), rowspan=2)
plt.title('Convolution')
convolved.plot()
thinkplot.config(xlabel='Time (s)')
thinkplot.save(root='sampling1',
formats=FORMATS,
legend=False)
def plot_filters(close):
"""Plots the filter that corresponds to diff, deriv, and integral.
"""
thinkplot.preplot(3, cols=2)
diff_window = np.array([1.0, -1.0])
diff_filter = make_filter(diff_window, close)
diff_filter.plot(label='diff')
deriv_filter = close.make_spectrum()
deriv_filter.hs = PI2 * 1j * deriv_filter.fs
deriv_filter.plot(label='derivative')
thinkplot.config(xlabel='Frequency (1/day)',
ylabel='Amplitude ratio',
loc='upper left')
thinkplot.subplot(2)
integ_filter = deriv_filter.copy()
integ_filter.hs = 1 / (PI2 * 1j * integ_filter.fs)
integ_filter.plot(label='integral')
thinkplot.config(xlabel='Frequency (1/day)',
ylabel='Amplitude ratio',
yscale='log')
thinkplot.save('diff_int3')
def aliasing_example(offset=0.000003):
"""Makes a figure showing the effect of aliasing.
"""
framerate = 10000
def plot_segment(freq):
signal = thinkdsp.CosSignal(freq)
duration = signal.period*4
thinkplot.Hlines(0, 0, duration, color='gray')
segment = signal.make_wave(duration, framerate=framerate*10)
segment.plot(linewidth=0.5, color='gray')
segment = signal.make_wave(duration, framerate=framerate)
segment.plot_vlines(label=freq, linewidth=4)
thinkplot.preplot(rows=2)
plot_segment(4500)
thinkplot.config(axis=[-0.00002, 0.0007, -1.05, 1.05])
thinkplot.subplot(2)
plot_segment(5500)
thinkplot.config(axis=[-0.00002, 0.0007, -1.05, 1.05])
thinkplot.save(root='aliasing1',
xlabel='Time (s)',
formats=FORMATS)
def triangle_example(freq):
"""Makes a figure showing a triangle wave.
freq: frequency in Hz
"""
framerate = 10000
signal = thinkdsp.TriangleSignal(freq)
duration = signal.period*3
segment = signal.make_wave(duration, framerate=framerate)
segment.plot()
thinkplot.save(root='triangle-%d-1' % freq,
xlabel='Time (s)',
axis=[0, duration, -1.05, 1.05])
wave = signal.make_wave(duration=0.5, framerate=framerate)
spectrum = wave.make_spectrum()
thinkplot.preplot(cols=2)
spectrum.plot()
thinkplot.config(xlabel='Frequency (Hz)',
ylabel='Amplitude')
thinkplot.subplot(2)
spectrum.plot()
thinkplot.config(ylim=[0, 500],
xlabel='Frequency (Hz)')
thinkplot.save(root='triangle-%d-2' % freq)
def main():
thinkdsp.random_seed(19)
signal = thinkdsp.BrownianNoise()
make_periodogram(signal)
return
signal = thinkdsp.UncorrelatedUniformNoise()
wave1 = signal.make_wave(duration=1.0, framerate=11025)
wave2 = signal.make_wave(duration=1.0, framerate=11025)
print wave1.cov(wave2)
print wave1.cov(wave1)
print wave2.cov(wave2)
print wave1.cov_mat(wave2)
print wave1.corr(wave2)
print wave1.corr(wave1)
print wave2.corr(wave2)
return
signal = thinkdsp.BrownianNoise()
process_noise(signal, root='red')
return
signal = thinkdsp.UncorrelatedUniformNoise()
process_noise(signal, root='white')
return
signal = thinkdsp.WhiteNoise()
white, integ_white = test_noise(signal, 'white-noise')
print white.estimate_slope()
signal = thinkdsp.BrownianNoise()
red, integ_red = test_noise(signal, 'red-noise')
print red.estimate_slope()
return
signal = thinkdsp.PinkNoise(beta=1.0)
pink, integ_pink = test_noise(signal, 'pink-noise')
print pink.estimate_slope()
thinkplot.preplot(num=3)
white.plot(low=1, exponent=2, label='white', linewidth=2)
pink.plot(low=1, exponent=2, label='pink', linewidth=2)
red.plot(low=1, exponent=2, label='red', linewidth=2)
thinkplot.show(xlabel='frequency (Hz)',
ylabel='power',
xscale='log',
yscale='log',
axis=[1, 18000, 1e-5, 1e8])
return
def main():
p1 = Hockey()
p2 = Hockey()
p1.UpdateSet([0,2,8,4])
p2.UpdateSet([1,3,1,0])
thinkplot.Clf()
thinkplot.preplot(num=2)
thinkplot.Pmf(p1)
thinkplot.Pmf(p2)
thinkplot.Save(root='hockey_self3',xlabel='',ylabel='Probability',formats=['pdf'])
def compute_corr(offset):
wave1 = make_sine(offset=0)
wave2 = make_sine(offset=-offset)
thinkplot.preplot(2)
wave1.segment(duration=0.01).plot()
wave2.segment(duration=0.01).plot()
corr = wave1.corr(wave2)
print('corr =', corr)
thinkplot.config(xlabel='Time (s)', ylim=[-1.05, 1.05])
def main():
thinkdsp.random_seed(19)
signal = thinkdsp.BrownianNoise()
make_periodogram(signal)
return
signal = thinkdsp.UncorrelatedUniformNoise()
wave1 = signal.make_wave(duration=1.0, framerate=11025)
wave2 = signal.make_wave(duration=1.0, framerate=11025)
print wave1.cov(wave2)
print wave1.cov(wave1)
print wave2.cov(wave2)
print wave1.cov_mat(wave2)
print wave1.corr(wave2)
print wave1.corr(wave1)
print wave2.corr(wave2)
return
signal = thinkdsp.BrownianNoise()
process_noise(signal, root='red')
return
signal = thinkdsp.UncorrelatedUniformNoise()
process_noise(signal, root='white')
return
signal = thinkdsp.WhiteNoise()
white, integ_white = test_noise(signal, 'white-noise')
print white.estimate_slope()
signal = thinkdsp.BrownianNoise()
red, integ_red = test_noise(signal, 'red-noise')
print red.estimate_slope()
return
signal = thinkdsp.PinkNoise(beta=1.0)
pink, integ_pink = test_noise(signal, 'pink-noise')
print pink.estimate_slope()
thinkplot.preplot(num=3)
white.plot(low=1, exponent=2, label='white', linewidth=2)
pink.plot(low=1, exponent=2, label='pink', linewidth=2)
red.plot(low=1, exponent=2, label='red', linewidth=2)
thinkplot.show(xlabel='frequency (Hz)',
ylabel='power',
xscale='log',
yscale='log',
axis=[1, 18000, 1e-5, 1e8])
return
def plot_shifted(wave, shift=0.002, start=0.2):
thinkplot.preplot(num=2)
segment1 = wave.segment(start=start, duration=0.01)
segment1.plot(linewidth=2, alpha=0.8)
segment2 = wave.segment(start=start-shift, duration=0.01)
segment2.plot(linewidth=2, alpha=0.4)
corr = segment1.corr(segment2)
text = r'$\rho =$ %.2g' % corr
thinkplot.text(0.0005, -0.8, text)
def process_noise(signal, root='white'):
"""Plots wave and spectrum for noise signals.
signal: Signal
root: string used to generate file names
"""
framerate = 11025
wave = signal.make_wave(duration=0.5, framerate=framerate)
# 0: waveform
segment = wave.segment(duration=0.1)
segment.plot(linewidth=1, alpha=0.5)
thinkplot.save(root=root+'noise0',
xlabel='Time (s)',
ylim=[-1.05, 1.05])
spectrum = wave.make_spectrum()
# 1: spectrum
spectrum.plot_power(linewidth=1, alpha=0.5)
thinkplot.save(root=root+'noise1',
xlabel='Frequency (Hz)',
ylabel='Power',
xlim=[0, spectrum.fs[-1]])
slope, _, _, _, _ = spectrum.estimate_slope()
print('estimated slope', slope)
# 2: integrated spectrum
integ = spectrum.make_integrated_spectrum()
integ.plot_power()
thinkplot.save(root=root+'noise2',
xlabel='Frequency (Hz)',
ylabel='Cumulative fraction of total power',
xlim=[0, framerate/2])
# 3: log-log power spectrum
spectrum.hs[0] = 0
thinkplot.preplot(cols=2)
spectrum.plot_power(linewidth=1, alpha=0.5)
thinkplot.config(xlabel='Frequency (Hz)',
ylabel='Power',
xlim=[0, framerate/2])
thinkplot.subplot(2)
spectrum.plot_power(linewidth=1, alpha=0.5)
thinkplot.config(xlabel='Frequency (Hz)',
xscale='log',
yscale='log',
xlim=[0, framerate/2])
thinkplot.save(root=root+'noise3')
def plot_diff_deriv(close):
change = thinkdsp.Wave(np.diff(close.ys), framerate=1)
deriv_spectrum = close.make_spectrum().differentiate()
deriv = deriv_spectrum.make_wave()
low, high = 0, 50
thinkplot.preplot(2)
thinkplot.plot(change.ys[low:high], label='diff')
thinkplot.plot(deriv.ys[low:high], label='derivative')
thinkplot.config(xlabel='Time (day)', ylabel='Price change ($)')
thinkplot.save('diff_int4')
def plot_diff_deriv(close):
change = thinkdsp.Wave(np.diff(close.ys), framerate=1)
deriv_spectrum = close.make_spectrum().differentiate()
deriv = deriv_spectrum.make_wave()
low, high = 0, 50
thinkplot.preplot(2)
thinkplot.plot(change.ys[low:high], label='diff')
thinkplot.plot(deriv.ys[low:high], label='derivative')
thinkplot.config(xlabel='Time (day)', ylabel='Price change ($)')
thinkplot.save('diff_int4')
def main():
locomotiveNumbers = range(1, 1001)
locomotive = Locomotive(locomotiveNumbers)
locomotive.Update(60)
locomotive.Update(160)
locomotive.Update(80)
locomotive.Update(570)
locomotive.Update(640)
print('Mean: {}'.format(locomotive.Mean()))
thinkplot.preplot(1)
thinkplot.Pmf(locomotive)
thinkplot.show(xlabel='Number of train', ylabel='Probability')
def plot_wave_and_spectrum(wave, root):
"""Makes a plot showing
"""
thinkplot.preplot(cols=2)
wave.plot()
thinkplot.config(xlabel="days", xlim=[0, 1650], ylabel="dollars", legend=False)
thinkplot.subplot(2)
spectrum = wave.make_spectrum()
print(spectrum.estimate_slope())
spectrum.plot()
thinkplot.config(xlabel="frequency (1/days)", ylabel="power", xscale="log", yscale="log", legend=False)
thinkplot.save(root=root)
def plot_shifted(wave, offset=0.001, start=0.2):
thinkplot.preplot(2)
segment1 = wave.segment(start=start, duration=0.01)
segment1.plot(linewidth=2, alpha=0.8)
# start earlier and then shift times to line up
segment2 = wave.segment(start=start-offset, duration=0.01)
segment2.shift(offset)
segment2.plot(linewidth=2, alpha=0.4)
corr = segment1.corr(segment2)
text = r'$\rho =$ %.2g' % corr
thinkplot.text(segment1.start+0.0005, -0.8, text)
thinkplot.config(xlabel='Time (s)', xlim=[start, start+duration], ylim=[-1, 1])
def process_noise(signal, root='white'):
"""Plots wave and spectrum for noise signals.
signal: Signal
root: string used to generate file names
"""
framerate = 48000
wave = signal.make_wave(duration=0.5, framerate=framerate)
# 0: waveform
segment = wave.segment(duration=0.1)
segment.plot(linewidth=1, alpha=0.5)
thinkplot.save(root=root + 'noise0', xlabel='Time (s)', ylim=[-1.05, 1.05])
spectrum = wave.make_spectrum()
# 1: spectrum
spectrum.plot_power(linewidth=1, alpha=0.5)
thinkplot.save(root=root + 'noise1',
xlabel='Frequency (Hz)',
ylabel='Power',
xlim=[0, spectrum.fs[-1]])
slope, _, _, _, _ = spectrum.estimate_slope()
print('estimated slope', slope)
# 2: integrated spectrum
integ = spectrum.make_integrated_spectrum()
integ.plot_power()
thinkplot.save(root=root + 'noise2',
xlabel='Frequency (Hz)',
ylabel='Cumulative fraction of total power',
xlim=[0, framerate / 2])
# 3: log-log power spectrum
spectrum.hs[0] = 0
thinkplot.preplot(cols=2)
spectrum.plot_power(linewidth=1, alpha=0.5)
thinkplot.config(xlabel='Frequency (Hz)',
ylabel='Power',
xlim=[0, framerate / 2])
thinkplot.subplot(2)
spectrum.plot_power(linewidth=1, alpha=0.5)
thinkplot.config(xlabel='Frequency (Hz)',
xscale='log',
yscale='log',
xlim=[0, framerate / 2])
thinkplot.save(root=root + 'noise3')
def plot_autocorr():
"""Plots autocorrelation for pink noise with different parameters
"""
numpy.random.seed(19)
thinkplot.preplot(3)
for beta in [1.2, 1.0, 0.7]:
label = r'$\beta$ = %.1f' % beta
plot_pink_autocorr(beta, label)
thinkplot.config(xlabel='lag',
ylabel='correlation',
xlim=[-1, 200],
ylim=[-0.05, 1.05])
thinkplot.save(root='autocorr4')
def plot_sawtooth_and_spectrum(wave, root):
"""Makes a plot showing a sawtoothwave and its spectrum.
"""
thinkplot.preplot(cols=2)
wave.plot()
thinkplot.config(xlabel='Time (s)')
thinkplot.subplot(2)
spectrum = wave.make_spectrum()
spectrum.plot()
thinkplot.config(xlabel='Frequency (Hz)',
ylabel='Amplitude',
xlim=[0, spectrum.fs[-1]])
thinkplot.save(root)
def plot_autocorr():
"""Plots autocorrelation for pink noise with different parameters
"""
numpy.random.seed(19)
thinkplot.preplot(3)
for beta in [1.2, 1.0, 0.7]:
label = r'$\beta$ = %.1f' % beta
plot_pink_autocorr(beta, label)
thinkplot.config(xlabel='lag',
ylabel='correlation',
xlim=[-1, 200],
ylim=[-0.05, 1.05])
thinkplot.save(root='autocorr4')
def overlapping_windows():
"""Makes a figure showing overlapping hamming windows.
"""
n = 256
window = np.hamming(n)
thinkplot.preplot(num=5)
start = 0
for i in range(5):
xs = np.arange(start, start + n)
thinkplot.plot(xs, window)
start += n / 2
thinkplot.save(root='windowing3', xlabel='Index', axis=[0, 800, 0, 1.05])
def overlapping_windows():
"""Makes a figure showing overlapping hamming windows.
"""
n = 256
window = numpy.hamming(n)
thinkplot.preplot(num=5)
start = 0
for i in range(5):
xs = numpy.arange(start, start + n)
thinkplot.plot(xs, window)
start += n / 2
thinkplot.save(root="windowing3", xlabel="time (s)", axis=[0, 800, 0, 1.05])
def plot_sawtooth_and_spectrum(wave, root):
"""Makes a plot showing a sawtoothwave and its spectrum.
"""
thinkplot.preplot(cols=2)
wave.plot()
thinkplot.config(xlabel='Time (s)')
thinkplot.subplot(2)
spectrum = wave.make_spectrum()
spectrum.plot()
thinkplot.config(xlabel='Frequency (Hz)',
ylabel='Amplitude',
xlim=[0, spectrum.fs[-1]])
thinkplot.save(root)
def make_figures():
"""Makes figures showing complex signals.
"""
amps = numpy.array([0.6, 0.25, 0.1, 0.05])
freqs = [100, 200, 300, 400]
framerate = 11025
ts = numpy.linspace(0, 1, framerate)
ys = synthesize1(amps, freqs, ts)
print(ys)
thinkplot.preplot(2)
n = framerate / 25
thinkplot.plot(ts[:n], ys[:n].real, label='real')
thinkplot.plot(ts[:n], ys[:n].imag, label='imag')
thinkplot.save(root='dft1',
xlabel='time (s)',
ylabel='wave',
ylim=[-1.05, 1.05])
ys = synthesize2(amps, freqs, ts)
amps2 = amps * numpy.exp(1.5j)
ys2 = synthesize2(amps2, freqs, ts)
thinkplot.preplot(2)
thinkplot.plot(ts[:n], ys.real[:n], label=r'$\phi_0 = 0$')
thinkplot.plot(ts[:n], ys2.real[:n], label=r'$\phi_0 = 1.5$')
thinkplot.save(root='dft2',
xlabel='time (s)',
ylabel='wave',
ylim=[-1.05, 1.05],
loc='lower right')
framerate = 10000
signal = thinkdsp.SawtoothSignal(freq=500)
wave = signal.make_wave(duration=0.1, framerate=framerate)
hs = dft(wave.ys)
amps = numpy.absolute(hs)
N = len(hs)
fs = numpy.arange(N) * framerate / N
thinkplot.plot(fs, amps)
thinkplot.save(root='dft3',
xlabel='frequency (Hz)',
ylabel='amplitude',
legend=False)
def plot_sincs(wave):
start = 1.0
duration = 0.01
factor = 4
short = wave.segment(start=start, duration=duration)
#short.plot()
sampled = sample(short, factor)
#sampled.plot_vlines(color='gray')
spectrum = sampled.make_spectrum(full=True)
boxcar = make_boxcar(spectrum, factor)
sinc = boxcar.make_wave()
sinc.shift(sampled.ts[0])
sinc.roll(len(sinc)//2)
thinkplot.preplot(2, cols=2)
sinc.plot()
thinkplot.config(xlabel='Time (s)')
thinkplot.subplot(2)
boxcar.plot()
thinkplot.config(xlabel='Frequency (Hz)',
ylim=[0, 1.05],
xlim=[-boxcar.max_freq, boxcar.max_freq])
thinkplot.save(root='sampling6',
formats=FORMATS)
return
# CAUTION: don't call plot_sinc_demo with a large wave or it will
# fill memory and crash
plot_sinc_demo(short, 4)
thinkplot.config(xlabel='Time (s)')
thinkplot.save(root='sampling7',
formats=FORMATS)
start = short.start + 0.004
duration = 0.00061
plot_sinc_demo(short, 4, start, duration)
thinkplot.config(xlabel='Time (s)',
xlim=[start, start+duration],
ylim=[-0.06, 0.17], legend=False)
thinkplot.save(root='sampling8',
formats=FORMATS)
def plot_amen2():
wave = thinkdsp.read_wave('263868__kevcio__amen-break-a-160-bpm.wav')
wave.normalize()
ax1 = thinkplot.preplot(6, rows=4)
wave.make_spectrum(full=True).plot(label='spectrum')
xlim = [-22050-250, 22050]
thinkplot.config(xlim=xlim, xticklabels='invisible')
ax2 = thinkplot.subplot(2)
impulses = make_impulses(wave, 4)
impulses.make_spectrum(full=True).plot(label='impulses')
thinkplot.config(xlim=xlim, xticklabels='invisible')
ax3 = thinkplot.subplot(3)
sampled = wave * impulses
spectrum = sampled.make_spectrum(full=True)
spectrum.plot(label='sampled')
thinkplot.config(xlim=xlim, xticklabels='invisible')
ax4 = thinkplot.subplot(4)
spectrum.low_pass(5512.5)
spectrum.plot(label='filtered')
thinkplot.config(xlim=xlim, xlabel='Frequency (Hz)')
thinkplot.save(root='sampling4',
formats=FORMATS)
def plot_integral(close):
deriv_spectrum = close.make_spectrum().differentiate()
integ_spectrum = deriv_spectrum.integrate()
print(integ_spectrum.hs[0])
integ_spectrum.hs[0] = 0
thinkplot.preplot(2)
integ_wave = integ_spectrum.make_wave()
close.plot(label='closing prices')
integ_wave.plot(label='integrated derivative')
thinkplot.config(xlabel='Time (day)', ylabel='Price ($)',
legend=True, loc='upper left')
thinkplot.save('diff_int5')
def main():
h1 = Hockey()
h2 = Hockey()
h1.UpdateSet([0, 2, 8, 4])
h2.UpdateSet([0, 1, 2, 3])
h1 = MakeGoalPmf(h1)
h2 = MakeGoalPmf(h2)
thinkplot.Clf()
thinkplot.preplot(num=2)
thinkplot.Pmf(h1)
thinkplot.Pmf(h2)
thinkplot.Save(root='hockey_self5_MakeGoalPmf',
xlabel='',
ylabel='Probability',
formats=['pdf'])
def plot_amen2():
wave = thinkdsp.read_wave('263868__kevcio__amen-break-a-160-bpm.wav')
wave.normalize()
ax1 = thinkplot.preplot(6, rows=4)
wave.make_spectrum(full=True).plot(label='spectrum')
xlim = [-22050 - 250, 22050]
thinkplot.config(xlim=xlim, xticklabels='invisible')
ax2 = thinkplot.subplot(2)
impulses = make_impulses(wave, 4)
impulses.make_spectrum(full=True).plot(label='impulses')
thinkplot.config(xlim=xlim, xticklabels='invisible')
ax3 = thinkplot.subplot(3)
sampled = wave * impulses
spectrum = sampled.make_spectrum(full=True)
spectrum.plot(label='sampled')
thinkplot.config(xlim=xlim, xticklabels='invisible')
ax4 = thinkplot.subplot(4)
spectrum.low_pass(5512.5)
spectrum.plot(label='filtered')
thinkplot.config(xlim=xlim, xlabel='Frequency (Hz)')
thinkplot.save(root='sampling4', formats=FORMATS)
def plot_diff_filters(wave):
window1 = np.array([1, -1])
window2 = np.array([-1, 4, -3]) / 2.0
window3 = np.array([2, -9, 18, -11]) / 6.0
window4 = np.array([-3, 16, -36, 48, -25]) / 12.0
window5 = np.array([12, -75, 200, -300, 300, -137]) / 60.0
thinkplot.preplot(5)
for i, window in enumerate([window1, window2, window3, window4, window5]):
padded = thinkdsp.zero_pad(window, len(wave))
fft_window = np.fft.rfft(padded)
n = len(fft_window)
thinkplot.plot(abs(fft_window)[:], label=i + 1)
thinkplot.show()
def plot_diff_filters(wave):
window1 = np.array([1, -1])
window2 = np.array([-1, 4, -3]) / 2.0
window3 = np.array([2, -9, 18, -11]) / 6.0
window4 = np.array([-3, 16, -36, 48, -25]) / 12.0
window5 = np.array([12, -75, 200, -300, 300, -137]) / 60.0
thinkplot.preplot(5)
for i, window in enumerate([window1, window2, window3, window4, window5]):
padded = thinkdsp.zero_pad(window, len(wave))
fft_window = np.fft.rfft(padded)
n = len(fft_window)
thinkplot.plot(abs(fft_window)[:], label=i+1)
thinkplot.show()
def make_figures():
"""Makes figures showing complex signals.
"""
amps = numpy.array([0.6, 0.25, 0.1, 0.05])
freqs = [100, 200, 300, 400]
framerate = 11025
ts = numpy.linspace(0, 1, framerate)
ys = synthesize1(amps, freqs, ts)
print(ys)
thinkplot.preplot(2)
n = framerate / 25
thinkplot.plot(ts[:n], ys[:n].real, label='real')
thinkplot.plot(ts[:n], ys[:n].imag, label='imag')
thinkplot.save(root='dft1',
xlabel='time (s)',
ylabel='wave',
ylim=[-1.05, 1.05])
ys = synthesize2(amps, freqs, ts)
amps2 = amps * numpy.exp(1.5j)
ys2 = synthesize2(amps2, freqs, ts)
thinkplot.preplot(2)
thinkplot.plot(ts[:n], ys.real[:n], label=r'$\phi_0 = 0$')
thinkplot.plot(ts[:n], ys2.real[:n], label=r'$\phi_0 = 1.5$')
thinkplot.save(root='dft2',
xlabel='time (s)',
ylabel='wave',
ylim=[-1.05, 1.05],
loc='lower right')
framerate = 10000
signal = thinkdsp.SawtoothSignal(freq=500)
wave = signal.make_wave(duration=0.1, framerate=framerate)
hs = dft(wave.ys)
amps = numpy.absolute(hs)
N = len(hs)
fs = numpy.arange(N) * framerate / N
thinkplot.plot(fs, amps)
thinkplot.save(root='dft3',
xlabel='frequency (Hz)',
ylabel='amplitude',
legend=False)
def show_impulses(wave, factor, i):
thinkplot.subplot(i)
thinkplot.preplot(2)
impulses = make_impulses(wave, factor)
impulses.segment(0, 0.001).plot_vlines(linewidth=2, xfactor=1000)
if i == 1:
thinkplot.config(title='Impulse train', ylim=[0, 1.05])
else:
thinkplot.config(xlabel='Time (ms)', ylim=[0, 1.05])
thinkplot.subplot(i + 1)
impulses.make_spectrum(full=True).plot()
kill_yticklabels()
if i == 1:
thinkplot.config(title='DFT of impulse train', xlim=[-22400, 22400])
else:
thinkplot.config(xlabel='Frequency (Hz)', xlim=[-22400, 22400])
def plot_shifted(wave, shift=0.002, start=0.2):
"""Plots two segments of a wave with different start times.
wave: Wave
shift: difference in start time (seconds)
start: start time in seconds
"""
thinkplot.preplot(num=2)
segment1 = wave.segment(start=start, duration=0.01)
segment1.plot(linewidth=2, alpha=0.8)
segment2 = wave.segment(start=start-shift, duration=0.01)
segment2.plot(linewidth=2, alpha=0.4)
corr = segment1.corr(segment2)
text = r'$\rho =$ %.2g' % corr
thinkplot.text(0.0005, -0.8, text)
thinkplot.config(xlabel='time (s)', ylim=[-1, 1])
def plot_shifted(wave, shift=0.002, start=0.2):
"""Plots two segments of a wave with different start times.
wave: Wave
shift: difference in start time (seconds)
start: start time in seconds
"""
thinkplot.preplot(num=2)
segment1 = wave.segment(start=start, duration=0.01)
segment1.plot(linewidth=2, alpha=0.8)
segment2 = wave.segment(start=start - shift, duration=0.01)
segment2.plot(linewidth=2, alpha=0.4)
corr = segment1.corr(segment2)
text = r'$\rho =$ %.2g' % corr
thinkplot.text(0.0005, -0.8, text)
thinkplot.config(xlabel='time (s)', ylim=[-1, 1])
def plot_gaussian():
"""Makes a plot showing the effect of convolution with a boxcar window.
"""
# start with a square signal
signal = thinkdsp.SquareSignal(freq=440)
wave = signal.make_wave(duration=1, framerate=44100)
spectrum = wave.make_spectrum()
# and a boxcar window
boxcar = np.ones(11)
boxcar /= sum(boxcar)
# and a gaussian window
gaussian = scipy.signal.gaussian(M=11, std=2)
gaussian /= sum(gaussian)
thinkplot.preplot(2)
thinkplot.plot(boxcar, label='boxcar')
thinkplot.plot(gaussian, label='Gaussian')
thinkplot.config(xlabel='Index', legend=True)
thinkplot.save(root='convolution7')
ys = np.convolve(wave.ys, gaussian, mode='same')
smooth = thinkdsp.Wave(ys, framerate=wave.framerate)
spectrum2 = smooth.make_spectrum()
# plot the ratio of the original and smoothed spectrum
amps = spectrum.amps
amps2 = spectrum2.amps
ratio = amps2 / amps
ratio[amps<560] = 0
# plot the same ratio along with the FFT of the window
padded = thinkdsp.zero_pad(gaussian, len(wave))
dft_gaussian = np.fft.rfft(padded)
thinkplot.plot(abs(dft_gaussian), color=GRAY, label='Gaussian filter')
thinkplot.plot(ratio, label='amplitude ratio')
thinkplot.config(xlabel='Frequency (Hz)',
ylabel='Amplitude ratio',
xlim=[0, 22050])
thinkplot.save(root='convolution8')
