ref: b3146dfd7eb0e914026e6674e6a3c06c00fc3203
dir: /python/demos/demo_yin_compare.py/
#! /usr/bin/env python
# -*- coding: utf8 -*-
""" Pure python implementation of the sum of squared difference
sqd_yin: original sum of squared difference [0]
d_t(tau) = x ⊗ kernel
sqd_yinfast: sum of squared diff using complex domain [0]
sqd_yinfftslow: tappered squared diff [1]
sqd_yinfft: modified squared diff using complex domain [1]
[0]:http://audition.ens.fr/adc/pdf/2002_JASA_YIN.pdf
[1]:https://aubio.org/phd/
"""
import sys
import numpy as np
import matplotlib.pyplot as plt
def sqd_yin(samples):
""" compute original sum of squared difference
Brute-force computation (cost o(N**2), slow)."""
B = len(samples)
W = B//2
yin = np.zeros(W)
for j in range(W):
for tau in range(1, W):
yin[tau] += (samples[j] - samples[j+tau])**2
return yin
def sqd_yinfast(samples):
""" compute approximate sum of squared difference
Using complex convolution (fast, cost o(n*log(n)) )"""
# yin_t(tau) = (r_t(0) + r_(t+tau)(0)) - 2r_t(tau)
B = len(samples)
W = B//2
yin = np.zeros(W)
sqdiff = np.zeros(W)
kernel = np.zeros(B)
# compute r_(t+tau)(0)
squares = samples**2
for tau in range(W):
sqdiff[tau] = squares[tau:tau+W].sum()
# add r_t(0)
sqdiff += sqdiff[0]
# compute r_t(tau) using kernel convolution in complex domain
samples_fft = np.fft.fft(samples)
kernel[1:W+1] = samples[W-1::-1] # first half, reversed
kernel_fft = np.fft.fft(kernel)
r_t_tau = np.fft.ifft(samples_fft * kernel_fft).real[W:]
# compute yin_t(tau)
yin = sqdiff - 2 * r_t_tau
return yin
def sqd_yintapered(samples):
""" compute tappered sum of squared difference
Brute-force computation (cost o(N**2), slow)."""
B = len(samples)
W = B//2
yin = np.zeros(W)
for tau in range(1, W):
for j in range(W - tau):
yin[tau] += (samples[j] - samples[j+tau])**2
return yin
def sqd_yinfft(samples):
""" compute yinfft modified sum of squared differences
Very fast, improved performance in transients.
FIXME: biased."""
B = len(samples)
W = B//2
yin = np.zeros(W)
def hanningz(W):
return .5 * (1. - np.cos(2. * np.pi * np.arange(W) / W))
#win = np.ones(B)
win = hanningz(B)
sqrmag = np.zeros(B)
fftout = np.fft.fft(win*samples)
sqrmag[0] = fftout[0].real**2
for l in range(1, W):
sqrmag[l] = fftout[l].real**2 + fftout[l].imag**2
sqrmag[B-l] = sqrmag[l]
sqrmag[W] = fftout[W].real**2
fftout = np.fft.fft(sqrmag)
sqrsum = 2.*sqrmag[:W + 1].sum()
yin[0] = 0
yin[1:] = sqrsum - fftout.real[1:W]
return yin / B
def cumdiff(yin):
""" compute the cumulative mean normalized difference """
W = len(yin)
yin[0] = 1.
cumsum = 0.
for tau in range(1, W):
cumsum += yin[tau]
if cumsum != 0:
yin[tau] *= tau/cumsum
else:
yin[tau] = 1
return yin
def compute_all(x):
import time
now = time.time()
yin = sqd_yin(x)
t1 = time.time()
print ("yin took %.2fms" % ((t1-now) * 1000.))
yinfast = sqd_yinfast(x)
t2 = time.time()
print ("yinfast took: %.2fms" % ((t2-t1) * 1000.))
yintapered = sqd_yintapered(x)
t3 = time.time()
print ("yintapered took: %.2fms" % ((t3-t2) * 1000.))
yinfft = sqd_yinfft(x)
t4 = time.time()
print ("yinfft took: %.2fms" % ((t4-t3) * 1000.))
return yin, yinfast, yintapered, yinfft
def plot_all(yin, yinfast, yintapered, yinfft):
fig, axes = plt.subplots(nrows=2, ncols=2, sharex=True, sharey='col')
axes[0, 0].plot(yin, label='yin')
axes[0, 0].plot(yintapered, label='yintapered')
axes[0, 0].set_ylim(bottom=0)
axes[0, 0].legend()
axes[1, 0].plot(yinfast, '-', label='yinfast')
axes[1, 0].plot(yinfft, label='yinfft')
axes[1, 0].legend()
axes[0, 1].plot(cumdiff(yin), label='yin')
axes[0, 1].plot(cumdiff(yintapered), label='yin tapered')
axes[0, 1].set_ylim(bottom=0)
axes[0, 1].legend()
axes[1, 1].plot(cumdiff(yinfast), '-', label='yinfast')
axes[1, 1].plot(cumdiff(yinfft), label='yinfft')
axes[1, 1].legend()
fig.tight_layout()
testfreqs = [441., 800., 10000., 40.]
if len(sys.argv) > 1:
testfreqs = map(float,sys.argv[1:])
for f in testfreqs:
print ("Comparing yin implementations for sine wave at %.fHz" % f)
samplerate = 44100.
win_s = 4096
x = np.cos(2.*np.pi * np.arange(win_s) * f / samplerate)
n_times = 1#00
for n in range(n_times):
yin, yinfast, yinfftslow, yinfft = compute_all(x)
if 0: # plot difference
plt.plot(yin-yinfast)
plt.tight_layout()
plt.show()
if 1:
plt.plot(yinfftslow-yinfft)
plt.tight_layout()
plt.show()
plot_all(yin, yinfast, yinfftslow, yinfft)
plt.show()