def get_chirp_wave_data(freq,
offset,
duration=0.1,
framerate=40000,
noise_ratio=0):
signal = thinkdsp.Chirp(start=freq * 0.5, end=1.5, amp=1.0)
wave = signal.make_wave(duration=duration, start=0, framerate=framerate)
if noise_ratio != 0:
wave.ys += numpy.random.standard_normal(wave.ys.shape) * noise_ratio
return wave.ys
def get_square_wave_data(freq,
offset,
duration=0.1,
framerate=40000,
noise_ratio=0):
signal = thinkdsp.SquareSignal(freq=freq, amp=1.0, offset=offset)
wave = signal.make_wave(duration=duration, start=0, framerate=framerate)
if noise_ratio != 0:
wave.ys += numpy.random.standard_normal(wave.ys.shape) * noise_ratio
return wave.ys
def rest(duration):
"""Makes a rest of the given duration.
duration: float seconds
returns: Wave
"""
signal = SilentSignal()
wave = signal.make_wave(duration)
return wave
def get_sawtooth_square_wave(freq, offset, duration=0.1, framerate=40000):
signal_sawtooth = thinkdsp.SawtoothSignal(freq=freq,
amp=1.0,
offset=offset)
signal_square = thinkdsp.SquareSignal(freq=freq,
amp=1.0,
offset=offset + 2 * numpy.pi * 0.2)
components = [signal_sawtooth, signal_square]
signal = thinkdsp.SumSignal(*components)
wave = signal.make_wave(duration=duration, start=0, framerate=40000)
wave.ys = wave.ys / len(components) # normalization
return wave.ys
def cos_wave(freq, duration=1, offset=0):
"""Makes a cosine wave with the given parameters.
freq: float cycles per second
duration: float seconds
offset: float radians
returns: Wave
"""
signal = CosSignal(freq, offset=offset)
wave = signal.make_wave(duration)
return wave
def make_chord(midi_nums, duration, sig_cons=CosSignal, framerate=11025):
"""Make a chord with the given duration.
midi_nums: sequence of int MIDI note numbers
duration: float seconds
sig_cons: Signal constructor function
framerate: int frames per second
returns: Wave
"""
freqs = [midi_to_freq(num) for num in midi_nums]
signal = sum(sig_cons(freq) for freq in freqs)
wave = signal.make_wave(duration, framerate=framerate)
wave.apodize()
return wave
def make_note(midi_num, duration, sig_cons=CosSignal, framerate=11025):
"""Make a MIDI note with the given duration.
midi_num: int MIDI note number
duration: float seconds
sig_cons: Signal constructor function
framerate: int frames per second
returns: Wave
"""
freq = midi_to_freq(midi_num)
signal = sig_cons(freq)
wave = signal.make_wave(duration, framerate=framerate)
wave.apodize()
return wave
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 = numpy.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', ylabel='amplitude')
thinkplot.save(root='convolution7')
ys = numpy.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 = zero_pad(gaussian, len(wave))
dft_gaussian = numpy.fft.rfft(padded)
thinkplot.plot(abs(dft_gaussian), color='0.7', label='Gaussian filter')
thinkplot.plot(ratio, label='amplitude ratio')
thinkplot.config(xlabel='frequency (Hz)',
ylabel='amplitude ratio',
xlim=[0, 22050],
legend=False)
thinkplot.save(root='convolution8')
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')
def make_wave(self, duration=1, start=0, framerate=11025):
"""Makes a Wave object.
duration: float seconds
start: float seconds
framerate: int frames per second
returns: Wave
"""
signal = UncorrelatedUniformNoise()
wave = signal.make_wave(duration, start, framerate)
spectrum = wave.make_spectrum()
spectrum.pink_filter(beta=self.beta)
wave2 = spectrum.make_wave()
wave2.unbias()
wave2.normalize(self.amp)
return wave2
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 = numpy.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", ylabel="amplitude")
thinkplot.save(root="convolution7")
ys = numpy.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 = zero_pad(gaussian, len(wave))
dft_gaussian = numpy.fft.rfft(padded)
thinkplot.plot(abs(dft_gaussian), color="0.7", label="Gaussian filter")
thinkplot.plot(ratio, label="amplitude ratio")
thinkplot.config(xlabel="frequency (Hz)", ylabel="amplitude ratio", xlim=[0, 22050], legend=False)
thinkplot.save(root="convolution8")
def plot_filter(M=11, std=2):
signal = thinkdsp.SquareSignal(freq=440)
wave = signal.make_wave(duration=1, framerate=44100)
spectrum = wave.make_spectrum()
gaussian = scipy.signal.gaussian(M=M, std=std)
gaussian /= sum(gaussian)
high = gaussian.max()
thinkplot.preplot(cols=2)
thinkplot.plot(gaussian)
thinkplot.config(xlabel='Index',
ylabel='Window',
xlim=[0, len(gaussian) - 1],
ylim=[0, 1.1 * high])
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.subplot(2)
thinkplot.plot(abs(dft_gaussian), color=GRAY, label='Gaussian filter')
thinkplot.plot(ratio, label='amplitude ratio')
thinkplot.show(xlabel='Frequency (Hz)',
ylabel='Amplitude ratio',
xlim=[0, 22050],
ylim=[0, 1.05])
import numpy as np import pandas as pd import scipy.signal np.set_printoptions(precision=3, suppress=True) # In[2]: PI2 = 2 * np.pi GRAY = '0.7' # In[3]: signal = thinkdsp.SquareSignal(freq=440) wave = signal.make_wave(duration=1, framerate=4400) segment = wave.segment(duration=0.01) # In[4]: window = np.ones(11) window /= sum(window) # In[5]: ys = segment.ys N = len(ys) padded = thinkdsp.zero_pad(window, N) # In[6]:
class TromboneGliss(Chirp):
def evaluate(self, ts):
f1, f2=1.0/self.start,1.0/self.end
lengths=np.linspace(f1,f2,len(ts))
freqs=1/lengths
dts=np.diff(ts,prepend=0)
dphis=PI2*freqs*dts
phases=np.cumsum(dphis)
ys=self.amp*np.cos(phases)
return ys
low=262
high=349
signal=TromboneGliss(high,low)
wave1=signal.make_wave(duration=1)
wave1.apodize()
wave1.write(filename="output3-5-1.wav")
signal=TromboneGliss(high,low)
wave2=signal.make_wave(duration=1)
wave2.apodize()
wave2.write(filename="output3-5-2.wav")
wave=wave1|wave2
wave.write(filename="output3-5-3.wav")
sp=wave.make_spectrum(1024)
sp.plot(high=1000)
plt.title("频率")
plt.show()
import thinkdsp
import matplotlib.pyplot as plt
import numpy as np
from scipy import signal
import wave
plt.rcParams['font.sans-serif'] = ['SimHei'] #图表上可以显示中文
plt.rcParams['axes.unicode_minus'] = False #图表上可以显示负号
PI2 = 2 * np.pi
class SawtoothChirp(Chirp):
def evaluate(self, ts):
freqs = np.linspace(self.start, self.end, len(ts))
dts = np.diff(ts, prepend=0)
dphis = PI2 * freqs * dts
phases = np.cumsum(dphis)
cycles = phases / PI2
frac, _ = np.modf(cycles)
ys = normalize(unbias(frac), self.amp)
return ys
signal = SawtoothChirp(start=2500, end=3000)
wave = signal.make_wave(duration=1, framerate=20000)
wave.write(filename="output3-3.wav")
wave.make_spectrum().plot()
plt.title("频率")
plt.show()
def plot_boxcar():
"""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)
# and a boxcar window
window = numpy.ones(11)
window /= sum(window)
# select a short segment of the wave
segment = wave.segment(duration=0.01)
# and pad with window out to the length of the array
padded = zero_pad(window, len(segment))
# compute the first element of the smoothed signal
prod = padded * segment.ys
print(sum(prod))
# compute the rest of the smoothed signal
smoothed = numpy.zeros_like(segment.ys)
rolled = padded
for i in range(len(segment.ys)):
smoothed[i] = sum(rolled * segment.ys)
rolled = numpy.roll(rolled, 1)
# plot the results
segment.plot(color="0.7")
smooth = thinkdsp.Wave(smoothed, framerate=wave.framerate)
smooth.plot()
thinkplot.config(ylim=[-1.05, 1.05], legend=False)
thinkplot.save(root="convolution2")
# compute the same thing using numpy.convolve
segment.plot(color="0.7")
ys = numpy.convolve(segment.ys, window, mode="valid")
smooth2 = thinkdsp.Wave(ys, framerate=wave.framerate)
smooth2.plot()
thinkplot.config(ylim=[-1.05, 1.05], legend=False)
thinkplot.save(root="convolution3")
# plot the spectrum before and after smoothing
spectrum = wave.make_spectrum()
spectrum.plot(color="0.7")
ys = numpy.convolve(wave.ys, window, mode="same")
smooth = thinkdsp.Wave(ys, framerate=wave.framerate)
spectrum2 = smooth.make_spectrum()
spectrum2.plot()
thinkplot.config(xlabel="frequency (Hz)", ylabel="amplitude", xlim=[0, 22050], legend=False)
thinkplot.save(root="convolution4")
# plot the ratio of the original and smoothed spectrum
amps = spectrum.amps
amps2 = spectrum2.amps
ratio = amps2 / amps
ratio[amps < 560] = 0
thinkplot.plot(ratio)
thinkplot.config(xlabel="frequency (Hz)", ylabel="amplitude ratio", xlim=[0, 22050], legend=False)
thinkplot.save(root="convolution5")
# plot the same ratio along with the FFT of the window
padded = zero_pad(window, len(wave))
dft_window = numpy.fft.rfft(padded)
thinkplot.plot(abs(dft_window), color="0.7", label="boxcar filter")
thinkplot.plot(ratio, label="amplitude ratio")
thinkplot.config(xlabel="frequency (Hz)", ylabel="amplitude ratio", xlim=[0, 22050], legend=False)
thinkplot.save(root="convolution6")
def plot_boxcar():
"""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)
# and a boxcar window
window = np.ones(11)
window /= sum(window)
# select a short segment of the wave
segment = wave.segment(duration=0.01)
# and pad with window out to the length of the array
N = len(segment)
padded = thinkdsp.zero_pad(window, N)
# compute the first element of the smoothed signal
prod = padded * segment.ys
print(sum(prod))
# compute the rest of the smoothed signal
smoothed = np.zeros(N)
rolled = padded
for i in range(N):
smoothed[i] = sum(rolled * segment.ys)
rolled = np.roll(rolled, 1)
# plot the results
segment.plot(color=GRAY)
smooth = thinkdsp.Wave(smoothed, framerate=wave.framerate)
smooth.plot()
thinkplot.config(xlabel='Time(s)', ylim=[-1.05, 1.05])
thinkplot.save(root='convolution2')
# compute the same thing using np.convolve
segment.plot(color=GRAY)
ys = np.convolve(segment.ys, window, mode='valid')
smooth2 = thinkdsp.Wave(ys, framerate=wave.framerate)
smooth2.plot()
thinkplot.config(xlabel='Time(s)', ylim=[-1.05, 1.05])
thinkplot.save(root='convolution3')
# plot the spectrum before and after smoothing
spectrum = wave.make_spectrum()
spectrum.plot(color=GRAY)
ys = np.convolve(wave.ys, window, mode='same')
smooth = thinkdsp.Wave(ys, framerate=wave.framerate)
spectrum2 = smooth.make_spectrum()
spectrum2.plot()
thinkplot.config(xlabel='Frequency (Hz)',
ylabel='Amplitude',
xlim=[0, 22050])
thinkplot.save(root='convolution4')
# plot the ratio of the original and smoothed spectrum
amps = spectrum.amps
amps2 = spectrum2.amps
ratio = amps2 / amps
ratio[amps<560] = 0
thinkplot.plot(ratio)
thinkplot.config(xlabel='Frequency (Hz)',
ylabel='Amplitude ratio',
xlim=[0, 22050])
thinkplot.save(root='convolution5')
# plot the same ratio along with the FFT of the window
padded = thinkdsp.zero_pad(window, len(wave))
dft_window = np.fft.rfft(padded)
thinkplot.plot(abs(dft_window), color=GRAY, label='DFT(window)')
thinkplot.plot(ratio, label='amplitude ratio')
thinkplot.config(xlabel='Frequency (Hz)',
ylabel='Amplitude ratio',
xlim=[0, 22050])
thinkplot.save(root='convolution6')
import wave
import thinkdsp
import matplotlib.pyplot as plt
import numpy as np
from scipy import signal
from thinkdsp import SinSignal, Spectrum, decorate
from thinkdsp import Signal
plt.rcParams['font.sans-serif']=['SimHei']#图表上可以显示中文
plt.rcParams['axes.unicode_minus']=False#图表上可以显示负号
signal=SinSignal(freq=440)
duration=signal.period*30.25
wave=signal.make_wave(duration)
for window_func in [np.bartlett,np.blackman,np.hanning,np.hamming]:
wave=signal.make_wave(duration)
wave.ys*=window_func(len(wave.ys))
Spectrum=wave.make_spectrum()
Spectrum.plot(high=880,label=window_func)
plt.title("频率")
plt.show()
def get_cosine_wave(freq, offset, duration=0.1, framerate=40000):
signal = thinkdsp.CosSignal(freq=freq, amp=1.0, offset=offset)
wave = signal.make_wave(duration=duration, start=0, framerate=framerate)
return wave.ys
from scipy.signal.spectral import periodogram
import thinkdsp
import matplotlib.pyplot as plt
import numpy as np
from scipy import signal
plt.rcParams['font.sans-serif'] = ['SimHei'] #图表上可以显示中文
plt.rcParams['axes.unicode_minus'] = False #图表上可以显示负号
signal = thinkdsp.SquareSignal(1100)
duration = 0.5
wave = signal.make_wave(duration, framerate=10000)
plt.subplot(1, 3, 1)
plt.title('1100HZ方波')
wave.plot()
wave.write(filename='output2-3.wav')
spectrum = wave.make_spectrum()
#spectrum=spectrum.mak
plt.subplot(1, 3, 3)
plt.title('采样后频谱')
spectrum.plot()
plt.show()
def plot_boxcar():
"""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)
# and a boxcar window
window = numpy.ones(11)
window /= sum(window)
# select a short segment of the wave
segment = wave.segment(duration=0.01)
# and pad with window out to the length of the array
padded = zero_pad(window, len(segment))
# compute the first element of the smoothed signal
prod = padded * segment.ys
print(sum(prod))
# compute the rest of the smoothed signal
smoothed = numpy.zeros_like(segment.ys)
rolled = padded
for i in range(len(segment.ys)):
smoothed[i] = sum(rolled * segment.ys)
rolled = numpy.roll(rolled, 1)
# plot the results
segment.plot(color='0.7')
smooth = thinkdsp.Wave(smoothed, framerate=wave.framerate)
smooth.plot()
thinkplot.config(ylim=[-1.05, 1.05], legend=False)
thinkplot.save(root='convolution2')
# compute the same thing using numpy.convolve
segment.plot(color='0.7')
ys = numpy.convolve(segment.ys, window, mode='valid')
smooth2 = thinkdsp.Wave(ys, framerate=wave.framerate)
smooth2.plot()
thinkplot.config(ylim=[-1.05, 1.05], legend=False)
thinkplot.save(root='convolution3')
# plot the spectrum before and after smoothing
spectrum = wave.make_spectrum()
spectrum.plot(color='0.7')
ys = numpy.convolve(wave.ys, window, mode='same')
smooth = thinkdsp.Wave(ys, framerate=wave.framerate)
spectrum2 = smooth.make_spectrum()
spectrum2.plot()
thinkplot.config(xlabel='frequency (Hz)',
ylabel='amplitude',
xlim=[0, 22050],
legend=False)
thinkplot.save(root='convolution4')
# plot the ratio of the original and smoothed spectrum
amps = spectrum.amps
amps2 = spectrum2.amps
ratio = amps2 / amps
ratio[amps < 560] = 0
thinkplot.plot(ratio)
thinkplot.config(xlabel='frequency (Hz)',
ylabel='amplitude ratio',
xlim=[0, 22050],
legend=False)
thinkplot.save(root='convolution5')
# plot the same ratio along with the FFT of the window
padded = zero_pad(window, len(wave))
dft_window = numpy.fft.rfft(padded)
thinkplot.plot(abs(dft_window), color='0.7', label='boxcar filter')
thinkplot.plot(ratio, label='amplitude ratio')
thinkplot.config(xlabel='frequency (Hz)',
ylabel='amplitude ratio',
xlim=[0, 22050],
legend=False)
thinkplot.save(root='convolution6')
import thinkdsp
import matplotlib.pyplot as plt
import numpy as np
from scipy import signal
plt.rcParams['font.sans-serif'] = ['SimHei'] #图表上可以显示中文
plt.rcParams['axes.unicode_minus'] = False #图表上可以显示负号
signal = thinkdsp.TriangleSignal(200) #200HZ的三角波
wave = signal.make_wave(duration=0.5, framerate=10000) #长度0.5，每秒10000次
period = signal.period
segment = wave.segment(start=0, duration=period * 3)
plt.subplot(2, 2, 1)
plt.title('200HZ三角波')
segment.plot()
spectrum = wave.make_spectrum()
plt.subplot(2, 2, 2)
plt.title('三角波频谱')
spectrum.plot()
#锯齿波
signal1 = thinkdsp.SawtoothSignal(200)
wave = signal1.make_wave(duration=0.5, framerate=10000)
period = signal1.period
segment = wave.segment(start=0, duration=period * 3)
plt.subplot(2, 2, 3)
plt.title('200HZ锯齿波')
segment.plot()
spectrum = wave.make_spectrum()
plt.subplot(2, 2, 4)
PI2 = 2 * np.pi
class SawtoothChirp(Chirp):
def evaluate(self, ts):
freqs = np.linspace(self.start, self.end, len(ts))
dts = np.diff(ts, prepend=0)
dphis = PI2 * freqs * dts
phases = np.cumsum(dphis)
cycles = phases / PI2
frac, _ = np.modf(cycles)
ys = normalize(unbias(frac), self.amp)
return ys
signal = SawtoothChirp(start=220, end=880)
wave = signal.make_wave(duration=0.1, framerate=4000)
wave.apodize()
wave.write(filename="output3-2.wav")
plt.subplot(1, 2, 1)
plt.title("SawtoothChirp")
wave.plot()
sp = wave.make_spectrum(256)
plt.subplot(1, 2, 2)
sp.plot()
plt.xlabel("时间")
plt.ylabel("频率")
plt.title("频谱")
plt.show()