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 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 make_randombursts(sfs = 2000, fs = 96000, intervals = 8):
"""
Assumes:
sfs frequency of the carrier wave
fs sampling frequency
intervals number of random bursts to be created
Returns:
Wave object consisting of beeps with random amplitude
"""
dt = 1/fs
final = np.array([])
for i in range(intervals):
amp = 1
wait = np.random.uniform(0.5,2)
stime = np.random.uniform(0.02,0.1)
t = np.arange(0,stime,dt)
zeros = np.zeros(int(np.floor(fs*wait)))
signal = amp*np.sin(t*np.pi*(1/stime))*np.sin(2*np.pi*t*sfs)
final = np.concatenate((final,zeros))
final = np.concatenate((final,signal))
final = np.concatenate((final,zeros))
final = np.concatenate((final, np.zeros(fs*2)))
return dsp.Wave(final, framerate = fs)
def f0(frame, audiofile):
threshold = 0.5
clip = td.Wave(frame)
spectrum = clip.make_spectrum()
#sorted_by_Hz = sorted(spectrum.peaks(), key=lambda tup: tup[1])
# to find F0 we can sort by Hz, unfortunately we have small readings at 0.0Hz
# and other small frequencies which make finding the true F0 hard
# remove the small amplitudes which don't well describe the energy in the sound.
# What is small is likely to be relative to the largest amplitude so use some threshold
greatest_Hz = (spectrum.peaks()[0])[0]
selected_pairs = []
list_pos = 0
while True:
pair = (spectrum.peaks()[list_pos])
within_threshold = (pair[0] > (greatest_Hz * threshold))
if within_threshold == False:
break
selected_pairs.append(pair)
list_pos = list_pos + 1
# selected_pairs is now a list of the pairs which have a prominent amplitude
sorted_by_Hz = sorted(selected_pairs, key=lambda tup: tup[1])
# the lowest Hz should now be F0, will need to tweek 0.5
return [sorted_by_Hz[0][1]]
def estimate(data):
length = len(data)
wave = thinkdsp.Wave(ys=data, framerate=Fs)
spectrum = wave.make_spectrum()
spectrum_heart = wave.make_spectrum()
spectrum_resp = wave.make_spectrum()
fft_mag = list(np.absolute(spectrum.hs))
fft_length = len(fft_mag)
spectrum_heart.high_pass(cutoff=0.5, factor=0)
spectrum_heart.low_pass(cutoff=4, factor=0)
fft_heart = list(np.absolute(spectrum_heart.hs))
max_fft_heart = max(fft_heart)
heart_sample = fft_heart.index(max_fft_heart)
hr = heart_sample * Fs / length * 60
spectrum_resp.high_pass(cutoff=0.15, factor=0)
spectrum_resp.low_pass(cutoff=0.5, factor=0)
fft_resp = list(np.absolute(spectrum_resp.hs))
max_fft_resp = max(fft_resp)
resp_sample = fft_resp.index(max_fft_resp)
rr = resp_sample * Fs / length * 60
if hr < 10:
return hr, 0
else:
return hr, rr
def testWaveAdd(self):
ys = np.array([1, 2, 3, 4])
wave1 = thinkdsp.Wave(ys, framerate=1)
wave2 = wave1.copy()
wave2.shift(2)
wave = wave1 + wave2
self.assertEqual(len(wave), 6)
self.assertAlmostEqual(sum(wave.ys), 20)
def sample(wave, factor):
"""Simulates sampling of a wave.
wave: Wave object
factor: ratio of the new framerate to the original
"""
ys = np.zeros(len(wave))
ys[::factor] = wave.ys[::factor]
ts = wave.ts[:]
return thinkdsp.Wave(ys, ts, wave.framerate)
def make_filter(window, wave):
"""Computes the filter that corresponds to a window.
window: NumPy array
wave: wave used to choose the length and framerate
returns: new Spectrum
"""
padded = thinkdsp.zero_pad(window, len(wave))
window_wave = thinkdsp.Wave(padded, framerate=wave.framerate)
window_spectrum = window_wave.make_spectrum()
return window_spectrum
def sdoa(wave1, wave2):
"""
Returns :
the number of samples of difference as calculated with the algorithm. If x is the result then this means
that wave 1 arrived before by x samples (negative means it arrived later)
Assumes:
Wave1 and Wave2 are wave objects with same number of samples
pass_band is the pass_band used for the filter. If nothing is passed the signals are not filtered.
"""
#creates the wave objects with the new signals
h1 = dsp.Wave(np.abs(Hilbert(wave1.ys)), framerate = wave1.framerate)
h2 = dsp.Wave(np.abs(Hilbert(wave2.ys)), framerate = wave2.framerate)
percentage = h1.duration * 0.001
start = percentage
duration = h1.duration - percentage
segment1 = h1.segment(start = start, duration = duration)
segment2 = h2.segment(start = start, duration = duration)
return (-1 )* correlate(h1,h2)
def hplot(wave1, wave2):
"""
Assummes
wave1 and wave2 are wave objects
Returns
Plot of wave1 and wave2 with respective envelopes obtained with hilbert Transforms
wave1 is in blue wave2 is in red. Envelope 1 is in black envelope 2 is in cyan
"""
#Remember to modify
h1 = dsp.Wave(np.abs(Hilbert(wave1.ys)), framerate = wave1.framerate)
h2 = dsp.Wave(np.abs(Hilbert(wave2.ys)), framerate = wave2.framerate)
plt.plot(wave1.ts, wave1.ys, color = 'b')
plt.plot(wave2.ts, wave2.ys, color = 'r')
plt.plot(h1.ts, h1.ys, color = 'k')
plt.plot(h2.ts, h2.ys, color = 'c')
plt.show()
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 testMakeSpectrum(self):
# rfft with n even
ys = np.arange(10)
wave = thinkdsp.Wave(ys, framerate=10)
spectrum = wave.make_spectrum()
self.assertAlmostEqual(spectrum.hs[0], 45)
wave2 = spectrum.make_wave()
#print(wave2.ys)
self.assertArrayAlmostEqual(wave.ys, wave2.ys)
# rfft with n odd
ys = np.arange(11)
wave = thinkdsp.Wave(ys, framerate=10)
spectrum = wave.make_spectrum()
self.assertAlmostEqual(spectrum.hs[0], 55)
# TODO: make rfft invertible when n is odd
#wave2 = spectrum.make_wave()
#print(wave2.ys)
#self.assertArrayAlmostEqual(wave.ys, wave2.ys)
# fft with n even
ys = np.arange(10)
wave = thinkdsp.Wave(ys, framerate=10)
spectrum = wave.make_spectrum(full=True)
self.assertAlmostEqual(spectrum.hs[0], 45)
wave2 = spectrum.make_wave()
#print(wave2.ys)
self.assertArrayAlmostEqual(wave.ys, wave2.ys)
# fft with n odd
ys = np.arange(11)
wave = thinkdsp.Wave(ys, framerate=10)
spectrum = wave.make_spectrum(full=True)
self.assertAlmostEqual(spectrum.hs[0], 55)
wave2 = spectrum.make_wave()
#print(wave2.ys)
self.assertArrayAlmostEqual(wave.ys, wave2.ys)
def apply_padding( self ):
"""
Adds the neccesary padding to the signal instance variable.
The variable used for the padding is that of the object when it is
instantiated.
"""
temp = self.signal.ys
#padding entry and exit time
pad_front = np.zeros(int(self.signal.framerate * self.tentry))
pad_back = np.zeros(int(self.signal.framerate * self.texit))
temp = np.concatenate((np.concatenate((pad_front, temp)), pad_back))
self.signal = dsp.Wave(temp, framerate= self.signal.framerate)
def main():
plot_convolution()
return
plot_response()
return
df = pandas.read_csv('coindesk-bpi-USD-close.csv',
nrows=1625,
parse_dates=[0])
ys = df.Close.values
wave = thinkdsp.Wave(ys, framerate=1)
#plot_wave_and_spectrum(wave, root='systems1')
diff = numpy.diff(ys)
wave2 = thinkdsp.Wave(diff, framerate=1)
#plot_wave_and_spectrum(wave2, root='systems2')
#plot_ratios(wave, wave2)
plot_derivative(wave, wave2)
return
plot_filters(wave)
def show_iq():
arr= np.fromfile(sys.argv[1], dtype=np.int16)#按8位数据读取iq数据
print(arr[0:100])
arr1=arr[0::2];
print(arr1[0:100])
arr2=arr[1::2];
print(arr2[0:100])
print(arr.size, arr1.size,arr2.size)
i = thinkdsp.Wave(arr1, framerate=2000000)
i.plot()
plt.show()
q = thinkdsp.Wave(arr1, framerate=2000000)
q.plot()
plt.show()
spectrum = i.make_spectrum()
spectrum.plot()
plt.show()
spectrum.low_pass(cutoff=100000, factor=0.01)
spectrum.plot()
plt.show()
violin_wave = spectrum.make_wave()
violin_wave.plot()
plt.show()
'''
real=arr[126500:128000:2]#取部分i数据
imag=arr[126501:128000:2]#取部分q数据
d_real=real.astype(np.float32)#数据类型转化，不然8位数据只能显示-127到127.卡了我一天不知道哪里错了
d_imag=imag.astype(np.float32)
comx=d_real+d_imag*1j#组成复数
'''
'''
def main():
names = ['date', 'open', 'high', 'low', 'close', 'volume']
df = pd.read_csv('fb.csv', header=0, names=names, parse_dates=[0])
ys = df.close.values[::-1]
close = thinkdsp.Wave(ys, framerate=1)
plot_wave_and_spectrum(close, root='diff_int1')
change = thinkdsp.Wave(np.diff(ys), framerate=1)
plot_wave_and_spectrum(change, root='diff_int2')
plot_filters(close)
plot_diff_deriv(close)
signal = thinkdsp.SawtoothSignal(freq=50)
in_wave = signal.make_wave(duration=0.1, framerate=44100)
plot_sawtooth_and_spectrum(in_wave, 'diff_int6')
out_wave = in_wave.cumsum()
out_wave.unbias()
plot_sawtooth_and_spectrum(out_wave, 'diff_int7')
plot_integral(close)
plot_ratios(in_wave, out_wave)
def plot_filter():
"""Plots the filter that corresponds to a 2-element moving average.
"""
impulse = np.zeros(8)
impulse[0] = 1
wave = thinkdsp.Wave(impulse, framerate=8)
impulse_spectrum = wave.make_spectrum(full=True)
window_array = np.array([
0.5,
0.5,
0,
0,
0,
0,
0,
0,
])
window = thinkdsp.Wave(window_array, framerate=8)
filtr = window.make_spectrum(full=True)
filtr.plot()
thinkplot.config(xlabel='Frequency', ylabel='Amplitude')
thinkplot.save('systems1')
def evalSymbReg(individual, target):
# Transform the tree expression in a callable function
func = toolbox.compile(expr=individual)
# Evaluate the mean squared error between the expression
# and the real function : x**4 + x**3 + x**2 + x
gen_ys = np.array([func(x, f) for x in t])
gen_sr = target.framerate
generated = thinkdsp.Wave(ys=gen_ys, framerate=gen_sr)
# gen_mfcc = getMFCC(gen_ys, gen_sr, False)
# target_mfcc = getMFCC(target.ys, target.framerate, False)
# result = mfcc_squared_error(gen_mfcc,target_mfcc)
# result = mfcc_squared_error(gen_ys,target.ys)
# result = mag_pha_s_error(target,generated)
result = features_diff(target, generated)
return result,
def synthesize_example():
amps = numpy.array([0.6, 0.25, 0.1, 0.05])
freqs = [100, 200, 300, 400]
framerate = 11025
ts = numpy.linspace(0, 1, 11025)
ys = synthesize2(amps, freqs, ts)
wave = thinkdsp.Wave(ys, framerate)
wave.normalize()
wave.apodize()
wave.play()
n = len(freqs)
amps2 = analyze1(ys[:n], freqs, ts[:n])
print amps
print amps2
def main():
random.seed(random.randint(1, 100))
pop = toolbox.population(n=500)
hof = tools.HallOfFame(1)
# CXPB - Probabilidade de crossover
# MUTPB - Probabilidade de mutação
# NGEN - Numero de gerações
CXPB, MUTPB, NGEN = 0.75, 0.12, 20
stats = tools.Statistics(lambda ind: ind.fitness.values)
stats.register("avg", np.mean)
stats.register("std", np.std)
stats.register("min", np.min)
stats.register("max", np.max)
pop, log = algorithms.eaSimple(pop,
toolbox,
CXPB,
MUTPB,
NGEN,
stats=stats,
halloffame=hof,
verbose=True)
# pop, log = algorithms.eaMuCommaLambda(population=pop,
# toolbox=toolbox,
# mu=200,
# lambda_=200,
# cxpb=CXPB,
# mutpb=MUTPB,
# ngen=NGEN,
# stats=mstats,
# halloffame=hof,
# verbose=True)
# pop, log = gp.harm(pop, toolbox, 0.5, 0.1, 40, alpha=0.05, beta=10, gamma=0.25, rho=0.9, stats=mstats,
# halloffame=hof, verbose=True)
# print log
function = gp.compile(hof[0], pset)
gen_ys = np.array([function(x, f) for x in t])
gen_sr = target.framerate
generated = thinkdsp.Wave(ys=gen_ys, framerate=gen_sr)
generated.write(filename="generated.wav")
#plot_log(log, 'aaa')
return pop, log, hof
def synthesize_example():
"""Synthesizes a sum of sinusoids and plays it.
"""
amps = np.array([0.6, 0.25, 0.1, 0.05])
fs = [100, 200, 300, 400]
framerate = 11025
ts = np.linspace(0, 1, 11025)
ys = synthesize2(amps, fs, ts)
wave = thinkdsp.Wave(ys, framerate)
wave.normalize()
wave.apodize()
wave.play()
n = len(fs)
amps2 = analyze1(ys[:n], fs, ts[:n])
print(amps)
print(amps2)
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 read_wave(filename='sound.wav'):
"""
Reads a file and creates a wave objec that is then assigned to the instance variable abs
representing the wave
"""
wavob = wavio.read(filename)
nchannel = len(wavob.data[0])
sampw = wavob.sampwidth
data = wavob.data
framerate = wavob.rate
ys = data[:,0]
if(nchannel >= 2):
ys = data[:,self.channel -1]
#ts = np.arange(len(ys)) / framerate
wav = dsp.Wave(ys, framerate=framerate)
wav.normalize()
self.wave = wav
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])
def f0(frame, audiofile):
#create a 'spectrum' list for the frame consisting of frequency/amplitude pairs
clip = td.Wave(frame)
spectrum = clip.make_spectrum()
# to find F0 we can sort by Hz, unfortunately we have small readings at 0.0Hz
# and other small frequencies which make finding the true F0 hard
# remove the small amplitudes which don't well describe the energy in the sound.
# What is small is likely to be relative to the largest amplitude so use some threshold
threshold = 0.5
#the pairs are sorted by amplitude, take the amplitude of the first pair as the greatest amplitude.
greatest_amp = (spectrum.peaks()[0])[0]
#a counter will be used to iterate over the positions of the list
list_pos = 0
#the pairs with amplitudes which are within the threshold will be copied to a new list
selected_pairs = []
while True:
#select the next pair from the list
pair = (spectrum.peaks()[list_pos])
#test whether the pair's amplitude is within the threshold
within_threshold = (pair[0] > (greatest_amp * threshold))
#if not within the threshold the loop can break as all followings pairs will have lower amplitudes
if within_threshold == False:
break
#if within the threshold add the pair to the list
selected_pairs.append(pair)
#increment the counter for the loop
list_pos = list_pos + 1
# selected_pairs is now a list of the pairs which have a prominent amplitude
sorted_by_Hz = sorted(selected_pairs, key=lambda tup: tup[1])
# the lowest Hz should now be F0
if len(sorted_by_Hz) == 0:
return [0]
else:
return [sorted_by_Hz[0][1]]
ys = segment.ys N = len(ys) padded = thinkdsp.zero_pad(window, N) # In[6]: prod = padded * ys # In[7]: sum(ys) # In[8]: convolved = np.convolve(ys, window, mode='valid') smooth2 = thinkdsp.Wave(convolved, framerate=wave.framerate) smooth2 # In[9]: spectrum = wave.make_spectrum() spectrum.plot(color='GRAY') # In[10]: convolved = np.convolve(wave.ys, window, mode='same') smooth = thinkdsp.Wave(convolved, framerate=wave.framerate) spectrum2 = smooth.make_spectrum() spectrum2.plot() # In[11]:
''' Get Emerson wave form data ''' wave_data = getEmersonWaveFormData(filePath) ''' Get Waveform parameters from Emerson data JSON''' wave_JSON = wave_data['signal'] dt_JSON = float(wave_data['deltaTime']) timeStamp_JSON = float(wave_data['timestamp']) N_wave_JSON = wave_data['len'] ''' Calculated parameters''' fs = 1 / dt_JSON duration = N_wave_JSON * dt_JSON ''' creating linear time vector to create a wave object''' t = np.linspace(0, duration, N_wave_JSON, endpoint=False) '''========================= Band-pass filter ==================================''' '''=====================================================================================''' ''' Creating a Wave object''' raw_wave = thinkdsp.Wave(ys=wave_JSON, ts=t, framerate=fs) ''' working with the wave object''' raw_wave.unbias() raw_wave.normalize() raw_wave.window(np.hanning(len(wave_JSON))) # windowing = Hanning ''' Creating a spectrum object from a wave object''' raw_spectrum = raw_wave.make_spectrum() ''' Filtering''' raw_spectrum.high_pass(400) raw_wave_filtered = raw_spectrum.make_wave() filtered_signal = raw_wave_filtered.ys ''' Signal Enveloping using hilbert transform''' analytic_signal = hilbert(filtered_signal) amplitude_envelope = np.abs(analytic_signal) instantaneous_phase = np.unwrap(np.angle(analytic_signal))
def stretch(wave, stretch_factor):
return thinkdsp.Wave(wave.ys,
wave.ts / stretch_factor,
framerate=wave.framerate * stretch_factor)
def demodulate_steps(wave):
'''
show the 8 plots of the demodulation process
:param wave: thinkdsp.Wave object
:return:
'''
# create a copy of the original wave
raw_wave = wave.copy()
# create a figure
fig = plt.figure()
# create a subplot
ax = fig.add_subplot(421)
# plot a segment of the raw_wave
raw_wave_segment = raw_wave.segment(0, 0.1)
raw_wave_segment.plot(label='raw wave', color='b')
# show legend label
ax.legend()
# make a spectrum from test wave
raw_spectrum = raw_wave.make_spectrum(full=False)
# create another subplot
ax = fig.add_subplot(422)
# plot the raw spectrum
raw_spectrum.plot(label='raw spectrum', color='g')
# show legend label
ax.legend()
# apply a high pass filter at 2kHz to the raw spectrum
raw_spectrum_filtered = raw_spectrum.copy()
raw_spectrum_filtered.high_pass(2000)
# create another subplot
ax = fig.add_subplot(424)
# plot the raw spectrum
raw_spectrum_filtered.plot(label='high pass', color='r')
# show legend label
ax.legend()
# make a time waveform from the filtered spectrum
raw_wave_filtered = raw_spectrum_filtered.make_wave()
# apply hanning windowing to the result waveform
raw_wave_filtered.window(np.hanning(len(raw_wave_filtered)))
# create another subplot
ax = fig.add_subplot(423)
# plot the raw spectrum
raw_wave_filtered_segment = raw_wave_filtered.segment(0, 0.01)
raw_wave_filtered.plot(label='high pass', color='c')
# show legend label
ax.legend()
# obtain the envelop of the result waveform
raw_wave_filtered_envelop = thinkdsp.Wave(
ys=np.abs(hilbert(raw_wave_filtered.ys)),
ts=raw_wave_filtered.ts,
framerate=raw_wave_filtered.framerate)
# create another subplot
ax = fig.add_subplot(425)
# plot the raw spectrum
raw_wave_filtered_envelop_segment = raw_wave_filtered_envelop.segment(
0, 0.01)
raw_wave_filtered_envelop.plot(label='envelop', color='m')
# show legend label
ax.legend()
# obtain the spectrum from the envelop
raw_spectrum_filtered_envelop = raw_wave_filtered_envelop.make_spectrum(
full=False)
# create another subplot
ax = fig.add_subplot(426)
# plot the raw spectrum
raw_spectrum_filtered_envelop.plot(label='envelop', color='y')
# show legend label
ax.legend()
# color option = one of these {'b', 'g', 'r', 'c', 'm', 'y', 'k', 'w'}
# show 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')