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 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 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_convolution():
response = thinkdsp.read_wave('180961__kleeb__gunshots.wav')
response = response.segment(start=0.26, duration=5.0)
response.normalize()
dt = 1
shift = dt * response.framerate
factor = 0.5
gun2 = response + shifted_scaled(response, shift, factor)
gun2.plot()
thinkplot.config(xlabel='time (s)',
ylabel='amplitude',
ylim=[-1.05, 1.05],
legend=False)
thinkplot.save(root='systems8')
signal = thinkdsp.SawtoothSignal(freq=410)
wave = signal.make_wave(duration=0.1, framerate=response.framerate)
total = 0
for j, y in enumerate(wave.ys):
total += shifted_scaled(response, j, y)
total.normalize()
wave.make_spectrum().plot(high=500, color='0.7', label='original')
segment = total.segment(duration=0.2)
segment.make_spectrum().plot(high=1000, label='convolved')
thinkplot.config(xlabel='frequency (Hz)', ylabel='amplitude')
thinkplot.save(root='systems9')
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 single_plot(dfs):
"""Make the plot.
"""
for i, age_group in enumerate(age_groups):
print(i, age_group)
series = [df.loc[age_group] for df in dfs]
models = [fit_row(s).fittedvalues for s in series]
xs = series[0].index + 2
rows = thinkstats2.PercentileRows(models, [5, 95])
thinkplot.fill_between(xs,
rows[0],
rows[1],
color=colors[i],
alpha=0.3)
rows = thinkstats2.PercentileRows(series, [50])
thinkplot.plot(xs,
rows[0],
label=labels[i],
color=colors[i],
alpha=0.6)
thinkplot.config(xlabel=xlabel, ylabel=ylabel, loc='upper left', axis=axis)
plt.gca().get_legend().set(title='Age group')
thinkplot.save(root='age_religion2')
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_facebook():
"""Plot Facebook prices and a smoothed time series.
"""
names = ['date', 'open', 'high', 'low', 'close', 'volume']
df = pd.read_csv('fb.csv', header=0, names=names, parse_dates=[0])
close = df.close.values[::-1]
dates = df.date.values[::-1]
days = (dates - dates[0]) / np.timedelta64(1,'D')
M = 30
window = np.ones(M)
window /= sum(window)
smoothed = np.convolve(close, window, mode='valid')
smoothed_days = days[M//2: len(smoothed) + M//2]
thinkplot.plot(days, close, color=GRAY, label='daily close')
thinkplot.plot(smoothed_days, smoothed, label='30 day average')
last = days[-1]
thinkplot.config(xlabel='Time (days)',
ylabel='Price ($)',
xlim=[-7, last+7],
legend=True,
loc='lower right')
thinkplot.save(root='convolution1')
def segment_spectrum(filename, start, duration=1.0):
"""Plots the spectrum of a segment of a WAV file.
Output file names are the given filename plus a suffix.
filename: string
start: start time in s
duration: segment length in s
"""
wave = thinkdsp.read_wave(filename)
plot_waveform(wave)
# extract a segment
segment = wave.segment(start, duration)
segment.ys = segment.ys[:1024]
print len(segment.ys)
segment.normalize()
segment.apodize()
spectrum = segment.make_spectrum()
segment.play()
# plot the spectrum
n = len(spectrum.hs)
spectrum.plot()
thinkplot.save(root=filename,
xlabel='frequency (Hz)',
ylabel='amplitude density')
def plot_pink_noise():
"""Makes a plot showing power spectrums for pink noise.
"""
thinkdsp.random_seed(20)
duration = 1.0
framerate = 512
signal = thinkdsp.UncorrelatedUniformNoise()
wave = signal.make_wave(duration=duration, framerate=framerate)
white = wave.make_spectrum()
signal = thinkdsp.PinkNoise()
wave = signal.make_wave(duration=duration, framerate=framerate)
pink = wave.make_spectrum()
signal = thinkdsp.BrownianNoise()
wave = signal.make_wave(duration=duration, framerate=framerate)
red = wave.make_spectrum()
linewidth = 1
white.plot_power(low=1, label='white', color='gray', linewidth=linewidth)
pink.plot_power(low=1, label='pink', color='pink', linewidth=linewidth)
red.plot_power(low=1, label='red', color='red', linewidth=linewidth)
thinkplot.save(root='noise-triple',
xlabel='frequency (Hz)',
ylabel='power',
xscale='log',
yscale='log',
axis=[1, 300, 1e-4, 1e5])
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_ratios(in_wave, out_wave):
# compare filters for cumsum and integration
diff_window = np.array([1.0, -1.0])
padded = thinkdsp.zero_pad(diff_window, len(in_wave))
diff_wave = thinkdsp.Wave(padded, framerate=in_wave.framerate)
diff_filter = diff_wave.make_spectrum()
cumsum_filter = diff_filter.copy()
cumsum_filter.hs = 1 / cumsum_filter.hs
cumsum_filter.plot(label='cumsum filter', color=GRAY, linewidth=7)
integ_filter = cumsum_filter.copy()
integ_filter.hs = integ_filter.framerate / (PI2 * 1j * integ_filter.fs)
integ_filter.plot(label='integral filter')
thinkplot.config(xlim=[0, integ_filter.max_freq],
yscale='log',
legend=True)
thinkplot.save('diff_int8')
# compare cumsum filter to actual ratios
cumsum_filter.plot(label='cumsum filter', color=GRAY, linewidth=7)
in_spectrum = in_wave.make_spectrum()
out_spectrum = out_wave.make_spectrum()
ratio_spectrum = out_spectrum.ratio(in_spectrum, thresh=1)
ratio_spectrum.plot(label='ratio', style='.', markersize=4)
thinkplot.config(xlabel='Frequency (Hz)',
ylabel='Amplitude ratio',
xlim=[0, integ_filter.max_freq],
yscale='log',
legend=True)
thinkplot.save('diff_int9')
def dct_plot():
signal = thinkdsp.TriangleSignal(freq=400)
wave = signal.make_wave(duration=1.0, framerate=10000)
dct = wave.make_dct()
dct.plot()
thinkplot.config(xlabel='Frequency (Hz)', ylabel='DCT')
thinkplot.save(root='dct1', formats=['pdf', 'eps'])
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 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 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 plot_pink_noise():
"""Makes a plot showing power spectrums for pink noise.
"""
thinkdsp.random_seed(20)
duration = 1.0
framerate = 512
def make_spectrum(signal):
wave = signal.make_wave(duration=duration, framerate=framerate)
spectrum = wave.make_spectrum()
spectrum.hs[0] = 0
return spectrum
signal = thinkdsp.UncorrelatedUniformNoise()
white = make_spectrum(signal)
signal = thinkdsp.PinkNoise()
pink = make_spectrum(signal)
signal = thinkdsp.BrownianNoise()
red = make_spectrum(signal)
linewidth = 2
# colorbrewer2.org 4-class sequential OrRd
white.plot_power(label='white', color='#fdcc8a', linewidth=linewidth)
pink.plot_power(label='pink', color='#fc8d59', linewidth=linewidth)
red.plot_power(label='red', color='#d7301f', linewidth=linewidth)
thinkplot.save(root='noise-triple',
xlabel='Frequency (Hz)',
ylabel='Power',
xscale='log',
yscale='log',
xlim=[1, red.fs[-1]])
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 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 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 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 plot_pink_noise():
"""Makes a plot showing power spectrums for pink noise.
"""
thinkdsp.random_seed(20)
duration = 1.0
framerate = 512
signal = thinkdsp.UncorrelatedUniformNoise()
wave = signal.make_wave(duration=duration, framerate=framerate)
white = wave.make_spectrum()
signal = thinkdsp.PinkNoise()
wave = signal.make_wave(duration=duration, framerate=framerate)
pink = wave.make_spectrum()
signal = thinkdsp.BrownianNoise()
wave = signal.make_wave(duration=duration, framerate=framerate)
red = wave.make_spectrum()
linewidth = 1
white.plot_power(low=1, label='white', color='gray', linewidth=linewidth)
pink.plot_power(low=1, label='pink', color='pink', linewidth=linewidth)
red.plot_power(low=1, label='red', color='red', linewidth=linewidth)
thinkplot.save(root='noise-triple',
xlabel='frequency (Hz)',
ylabel='power',
xscale='log',
yscale='log',
axis=[1, 300, 1e-4, 1e5])
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 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 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_ratios(in_wave, out_wave):
# compare filters for cumsum and integration
diff_window = np.array([1.0, -1.0])
padded = thinkdsp.zero_pad(diff_window, len(in_wave))
diff_wave = thinkdsp.Wave(padded, framerate=in_wave.framerate)
diff_filter = diff_wave.make_spectrum()
cumsum_filter = diff_filter.copy()
cumsum_filter.hs = 1 / cumsum_filter.hs
cumsum_filter.plot(label='cumsum filter', color=GRAY, linewidth=7)
integ_filter = cumsum_filter.copy()
integ_filter.hs = integ_filter.framerate / (PI2 * 1j * integ_filter.fs)
integ_filter.plot(label='integral filter')
thinkplot.config(xlim=[0, integ_filter.max_freq],
yscale='log', legend=True)
thinkplot.save('diff_int8')
# compare cumsum filter to actual ratios
cumsum_filter.plot(label='cumsum filter', color=GRAY, linewidth=7)
in_spectrum = in_wave.make_spectrum()
out_spectrum = out_wave.make_spectrum()
ratio_spectrum = out_spectrum.ratio(in_spectrum, thresh=1)
ratio_spectrum.plot(label='ratio', style='.', markersize=4)
thinkplot.config(xlabel='Frequency (Hz)',
ylabel='Amplitude ratio',
xlim=[0, integ_filter.max_freq],
yscale='log', legend=True)
thinkplot.save('diff_int9')
def plot_facebook():
"""Plot Facebook prices and a smoothed time series.
"""
names = ['date', 'open', 'high', 'low', 'close', 'volume']
df = pd.read_csv('fb.csv', header=0, names=names, parse_dates=[0])
close = df.close.values[::-1]
dates = df.date.values[::-1]
days = (dates - dates[0]) / np.timedelta64(1,'D')
M = 30
window = np.ones(M)
window /= sum(window)
smoothed = np.convolve(close, window, mode='valid')
smoothed_days = days[M//2: len(smoothed) + M//2]
thinkplot.plot(days, close, color=GRAY, label='daily close')
thinkplot.plot(smoothed_days, smoothed, label='30 day average')
last = days[-1]
thinkplot.config(xlabel='Time (days)',
ylabel='Price ($)',
xlim=[-7, last+7],
legend=True,
loc='lower right')
thinkplot.save(root='convolution1')
def segment_spectrum(filename, start, duration=1.0):
"""Plots the spectrum of a segment of a WAV file.
Output file names are the given filename plus a suffix.
filename: string
start: start time in s
duration: segment length in s
"""
wave = thinkdsp.read_wave(filename)
plot_waveform(wave)
# extract a segment
segment = wave.segment(start, duration)
segment.ys = segment.ys[:1024]
print len(segment.ys)
segment.normalize()
segment.apodize()
spectrum = segment.make_spectrum()
segment.play()
# plot the spectrum
n = len(spectrum.hs)
spectrum.plot()
thinkplot.save(root=filename,
xlabel='frequency (Hz)',
ylabel='amplitude density')
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 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_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 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 plot_pink_noise():
"""Makes a plot showing power spectrums for pink noise.
"""
thinkdsp.random_seed(20)
duration = 1.0
framerate = 512
def make_spectrum(signal):
wave = signal.make_wave(duration=duration, framerate=framerate)
spectrum = wave.make_spectrum()
spectrum.hs[0] = 0
return spectrum
signal = thinkdsp.UncorrelatedUniformNoise()
white = make_spectrum(signal)
signal = thinkdsp.PinkNoise()
pink = make_spectrum(signal)
signal = thinkdsp.BrownianNoise()
red = make_spectrum(signal)
linewidth = 2
white.plot_power(label='white', color='#9ecae1', linewidth=linewidth)
pink.plot_power(label='pink', color='#4292c6', linewidth=linewidth)
red.plot_power(label='red', color='#2171b5', linewidth=linewidth)
thinkplot.save(root='noise-triple',
xlabel='Frequency (Hz)',
ylabel='Power',
xscale='log',
yscale='log',
xlim=[1, red.fs[-1]])
def plot_convolution():
response = thinkdsp.read_wave("180961__kleeb__gunshots.wav")
response = response.segment(start=0.26, duration=5.0)
response.normalize()
dt = 1
shift = dt * response.framerate
factor = 0.5
gun2 = response + shifted_scaled(response, shift, factor)
gun2.plot()
thinkplot.config(xlabel="time (s)", ylabel="amplitude", ylim=[-1.05, 1.05], legend=False)
thinkplot.save(root="systems8")
signal = thinkdsp.SawtoothSignal(freq=410)
wave = signal.make_wave(duration=0.1, framerate=response.framerate)
total = 0
for j, y in enumerate(wave.ys):
total += shifted_scaled(response, j, y)
total.normalize()
wave.make_spectrum().plot(high=500, color="0.7", label="original")
segment = total.segment(duration=0.2)
segment.make_spectrum().plot(high=1000, label="convolved")
thinkplot.config(xlabel="frequency (Hz)", ylabel="amplitude")
thinkplot.save(root="systems9")
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 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)
spectrum = wave.make_spectrum()
spectrum.plot(high=660)
thinkplot.save("chirp1", xlabel="frequency (Hz)", ylabel="amplitude")
def dct_plot():
signal = thinkdsp.TriangleSignal(freq=400)
wave = signal.make_wave(duration=1.0, framerate=10000)
dct = wave.make_dct()
dct.plot()
thinkplot.config(xlabel='Frequency (Hz)', ylabel='DCT')
thinkplot.save(root='dct1',
formats=['pdf', 'eps'])
def plot_diff_filter(close):
"""Plots the filter that corresponds to first order finite difference.
"""
diff_window = np.array([1.0, -1.0])
diff_filter = make_filter(diff_window, close)
diff_filter.plot()
thinkplot.config(xlabel='Frequency (1/day)', ylabel='Amplitude ratio')
thinkplot.save('diff_int3')
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)
spectrum = wave.make_spectrum()
spectrum.plot(high=660)
thinkplot.save('chirp1', xlabel='frequency (Hz)', ylabel='amplitude')
def plot(res, index):
slices = [[0, None], [400, 1000], [860, 900]]
start, end = slices[index]
xs, ys = zip(*res[start:end])
thinkplot.plot(xs, ys)
thinkplot.save(root='dft%d' % index,
xlabel='freq (Hz)',
ylabel='cov',
formats=['png'])
def plot(res, index):
slices = [[0, None], [400, 1000], [860, 900]]
start, end = slices[index]
xs, ys = zip(*res[start:end])
thinkplot.plot(xs, ys)
thinkplot.save(root='dft%d' % index,
xlabel='freq (Hz)',
ylabel='cov',
formats=['png'])
def plot_convolution(response):
"""Plots the impulse response and a shifted, scaled copy.
"""
shift = 1
factor = 0.5
gun2 = response + shifted_scaled(response, shift, factor)
gun2.plot()
thinkplot.config(xlabel='Time (s)', ylim=[-1.05, 1.05], legend=False)
thinkplot.save(root='systems8')
def main():
"""main."""
dataset = [30, 60, 90]
for high in [500, 1000, 2000]:
suite = make_posterior(high, dataset)
print(high, suite.mean())
thinkplot.save(root='train2',
xlabel='Number of trains',
ylabel='Probability')
def violin_spectrogram():
"""Makes a spectrogram of a violin recording.
"""
wave = thinkdsp.read_wave("92002__jcveliz__violin-origional.wav")
seg_length = 2048
spectrogram = wave.make_spectrogram(seg_length)
spectrogram.plot(high=seg_length / 8)
# TODO: try imshow?
thinkplot.save("spectrogram1", xlabel="time (s)", ylabel="frequency (Hz)", formats=["pdf"])
def plot_waveform(wave, start=1.30245, duration=0.00683):
"""Plots a short window from a wave.
duration: float
"""
segment = wave.segment(start, duration)
segment.normalize()
segment.plot()
thinkplot.save(root='waveform',
xlabel='time (s)',
axis=[0, duration, -1.05, 1.05])
def plot_convolution(response):
"""Plots the impulse response and a shifted, scaled copy.
"""
shift = 1
factor = 0.5
gun2 = response + shifted_scaled(response, shift, factor)
gun2.plot()
thinkplot.config(xlabel='Time (s)',
ylim=[-1.05, 1.05],
legend=False)
thinkplot.save(root='systems8')
def plot_sampling(wave, root):
ax1 = thinkplot.preplot(2, rows=2)
wave.make_spectrum(full=True).plot(label='spectrum')
thinkplot.config(xlim=XLIM, xticklabels='invisible')
ax2 = thinkplot.subplot(2)
sampled = sample(wave, 4)
sampled.make_spectrum(full=True).plot(label='sampled')
thinkplot.config(xlim=XLIM, xlabel='Frequency (Hz)')
thinkplot.save(root=root, formats=FORMATS)
def main():
gss = utils.ReadGss('gss_college_religion')
diffs = [run(gss) for _ in range(101)]
years = diffs[0].index
rows = thinkstats2.PercentileRows(diffs, [5, 50, 95])
thinkplot.fill_between(years, rows[0], rows[2], alpha=0.2)
thinkplot.plot(years, rows[1])
thinkplot.config(xlabel='Year',
ylabel='Difference in fraction with no affiliation',
xlim=[1970, 2018])
thinkplot.save(root='college_religion')
def plot_waveform(wave, start=1.30245, duration=0.00683):
"""Plots a short window from a wave.
duration: float
"""
segment = wave.segment(start, duration)
segment.normalize()
segment.plot()
thinkplot.save(root='waveform',
xlabel='time (s)',
axis=[0, duration, -1.05, 1.05])
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 plot_sampling(wave, root):
ax1 = thinkplot.preplot(2, rows=2)
wave.make_spectrum(full=True).plot(label='spectrum')
thinkplot.config(xlim=XLIM, xticklabels='invisible')
ax2 = thinkplot.subplot(2)
sampled = sample(wave, 4)
sampled.make_spectrum(full=True).plot(label='sampled')
thinkplot.config(xlim=XLIM, xlabel='Frequency (Hz)')
thinkplot.save(root=root,
formats=FORMATS)
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 chirp_spectrogram():
"""Makes a spectrogram of a one-second one-octave linear chirp.
"""
signal = thinkdsp.Chirp(start=220, end=440)
wave = signal.make_wave(duration=1, framerate=11025)
spectrogram = wave.make_spectrogram(seg_length=512)
print "time res", spectrogram.time_res
print "freq res", spectrogram.freq_res
print "product", spectrogram.time_res * spectrogram.freq_res
spectrogram.plot(high=32)
thinkplot.save("chirp2", xlabel="time (s)", ylabel="frequency (Hz)")
def plot_power_density(root, spectrum):
"""
"""
# 4: CDF of power density
cdf = thinkstats2.MakeCdfFromList(spectrum.power)
thinkplot.cdf(cdf)
thinkplot.save(root=root + 'noise4', xlabel='power density', ylabel='CDF')
# 5: CCDF of power density, log-y
thinkplot.cdf(cdf, complement=True)
thinkplot.save(root=root + 'noise5',
xlabel='power density',
ylabel='log(CCDF)',
yscale='log')
def main():
"""main."""
hypos = range(1, 1001)
suite = Train(hypos)
suite.update(60)
print(suite.mean())
thinkplot.pre_plot(1)
thinkplot.pmf(suite)
thinkplot.save(root='train1',
xlabel='Number of trains',
ylabel='Probability',
formats=['pdf', 'eps'])
def chirp_spectrogram():
"""Makes a spectrogram of a one-second one-octave linear chirp.
"""
signal = thinkdsp.Chirp(start=220, end=440)
wave = signal.make_wave(duration=1, framerate=11025)
spectrogram = wave.make_spectrogram(seg_length=512)
print('time res', spectrogram.time_res)
print('freq res', spectrogram.freq_res)
print('product', spectrogram.time_res * spectrogram.freq_res)
spectrogram.plot(high=32)
thinkplot.save('chirp2', xlabel='time (s)', ylabel='frequency (Hz)')
def plot_suites(suites, root):
"""Plot two suites.
suite1, suite2: Suite objects
root: string filename to write
"""
thinkplot.clear_figure()
thinkplot.pre_plot(len(suites))
thinkplot.pmfs(suites)
thinkplot.save(root=root,
xlabel='x',
ylabel='Probability',
formats=['pdf', 'eps'])
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')
