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music.py
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music.py
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# -*- coding: utf-8 -*-
"""
Created on Tue Feb 20 12:55:11 2018
@author: wattai
"""
import numpy as np
import matplotlib.pyplot as plt
np.random.seed(7)
class MUSIC():
def __init__(self, fs, d, c=340., N_theta=180):
self.fs = fs # sampling frequency [Hz].
self.T = 1. / fs # sampling Term [sec].
self.d = d # mic. distance [m].
self.k = None # data index series [point].
self.L = None # data length [point].
self.c = c # sound speed [m/sec].
self.N_theta = N_theta
self.N_ch = None
self.minvec = None
self.thetas = None
def alpha(self, theta):
return np.array([np.ones(len(self.k)),
np.exp(2j * np.pi * self.d * np.sin(theta)
/ (self.c * self.T)
* ((self.k) / (len(self.k)*2)))
])
def S_MN(self, thetas):
return np.array([1.
/ np.abs(self.minvec.conj().transpose(0, 2, 1) @ self.alpha(theta).transpose(1, 0).reshape(-1, self.N_ch, 1)).squeeze()**2
for theta in thetas]).T * np.sqrt(self.eigval[:, 0][:, None] / (self.eigval[:, -1][:, None]+1e-8) )
def S_MUSIC(self, thetas):
return np.array([
np.sum(self.alpha(theta).conj() * self.alpha(theta), axis=0) \
/ np.abs(self.minvec.conj().transpose(0, 2, 1) @ self.alpha(theta).transpose(1, 0).reshape(-1, self.N_ch, 1)).squeeze()**2
for theta in thetas]).T * np.sqrt(self.eigval[:, 0][:, None])# / (self.eigval[:, -1][:, None]+1e-8) )
def fit_transform(self, x):
# x: input sound signal
# x.shape = (sample, N_ch)
self.L = len(x)//1
self.k = np.arange(self.L//2)
self.N_ch = x.shape[1]
winfunc = np.hanning(len(x)).reshape(-1, 1)
X = np.fft.fft(winfunc * x, axis=0)[:self.L//2, :]
self.R = (X.conj().reshape(-1, self.N_ch, 1) @ X.reshape(-1, 1, self.N_ch)) \
/ (X.shape[0] / self.fs)
self.eigval, self.eigvec = np.linalg.eig(self.R)
self.minvec = self.eigvec[:, :, -1].reshape(-1, self.N_ch, 1)
self.thetas = np.linspace(-np.pi/2, np.pi/2, self.N_theta)
#self.S = self.S_MN(self.thetas)
self.S = self.S_MUSIC(self.thetas)
return self.S
def theta_hat(self):
return np.rad2deg(self.thetas[(np.abs(self.S)**2).mean(0).argmax()])
def CSP(x):
phi = np.correlate(x[:, 0], x[:, 1], mode='full')
PHI = np.fft.fft(phi)
csp = np.fft.fft(PHI / np.abs(PHI)).real
return csp
def TDOA(x):
estimated_delay = (CSP(x).argmax() - (len(x[:, 0])))
return estimated_delay
def tdoa2deg(tdoa, c=340, d=0.1):
return np.rad2deg(np.arccos(np.clip(tdoa*c/d, -1, 1)))
def deg2tdoa(deg, c=340, d=0.1):
return d*np.cos(np.deg2rad(deg))/c
def simu_csp(theta=120, fs=16000, N_fft=128, c=340, d=1.0):
tdoa = deg2tdoa(theta, c=c, d=d)
width = N_fft // 2
t = np.linspace(0, N_fft+2*width-1, N_fft+2*width) / fs # base time.
s = np.random.randn(N_fft + 2*width) # signal source.
ptdoa = np.round(tdoa*fs).astype('i') # point of TDOA.
t1 = t[width+ptdoa : width+ptdoa+N_fft]
#t2 = t[width : width+N]
x1 = s[width+ptdoa : width+ptdoa+N_fft] + 0.5*np.random.randn(len(t1))
x2 = s[width : width+N_fft] + 0.5*np.random.randn(len(t1))
x = np.c_[x1, x2]
theta_hat = tdoa2deg(TDOA(x)/fs, c=c, d=d)
csp = CSP(x)
N_csp = len(csp)
csp /= N_csp
t_delay = np.linspace(-N_csp//2, N_csp//2, N_csp) / fs
theta_delay = tdoa2deg(t_delay, c=c, d=d)
plt.figure()
plt.subplot(211)
plt.title('Based on CSP.')
plt.plot(t1, x1, linestyle='-', label='1ch')
plt.plot(t1, x2, linestyle='-.', label='2ch')
plt.legend(loc='upper right')
plt.xlabel('time [sec]')
plt.ylabel('amp. [a.u.]')
plt.xlim(t1.min(), t1.max())
plt.grid(linestyle='--')
plt.subplot(212)
plt.plot((90-theta_delay), 10*np.log10((csp**2)/(csp**2).max()),
marker="D", markersize=5)
plt.xlabel('theta delay [deg]')
plt.ylabel('CSP log power [dB]')
plt.xlim(90-theta_delay.max(), 90-theta_delay.min())
plt.grid(linestyle='--')
plt.tight_layout()
plt.show()
print("theta: %.3f, theta_hat: %.3f" % (90-theta, 90-theta_hat))
def simu_music(theta=120, fs=16000, N_fft=128, c=340, d=1.0, N_theta=90+1):
tdoa = d*np.cos(np.deg2rad(theta))/c
width = N_fft // 2
#s = np.random.randn(N_fft + 2*width) # signal source.
ptdoa = np.round(tdoa*fs).astype('i') # point of TDOA.
t = np.linspace(0, N_fft+2*width-1, N_fft+2*width) / fs # base time.
t1 = t[width+ptdoa : width+N_fft+ptdoa]
t2 = t[width : width+N_fft]
x1 = 1*np.sin(2*np.pi*500*t1)[:, None] + 0.01*np.random.randn(len(t1))[:, None]
x2 = 1*np.sin(2*np.pi*500*t2)[:, None] + 0.01*np.random.randn(len(t2))[:, None]
#x1 = s[width+ptdoa : width+ptdoa+N_fft][:, None] + 0.01*np.random.randn(len(t1))[:, None]
#x2 = s[width : width+N_fft][:, None] + 0.01*np.random.randn(len(t2))[:, None]
x = np.c_[x1, x2]
est = MUSIC(fs=fs, d=d, c=c, N_theta=N_theta)
S = est.fit_transform(x)
#eps = 1e-8
plt.figure()
plt.subplot(211)
plt.title('Based on MUSIC.')
X, Y = np.meshgrid(np.rad2deg(est.thetas),
np.linspace(0, fs//2-1, len(x)//2))
plt.pcolor(X, Y,
(np.abs(S)), cmap='jet')
plt.colorbar()
plt.xlim(-90, 90)
plt.grid(linestyle='--')
plt.ylabel('frequency [Hz]')
plt.xlabel('angle [deg]')
plt.subplot(212)
P = 10*np.log10((np.abs(S)**2).mean(0) / (np.abs(S)**2).mean(0).max())
plt.plot(np.rad2deg(est.thetas), P,
marker="D", markersize=5)
plt.xlim(-90, 90)
plt.grid(linestyle='--')
plt.ylabel('log-power spec. [dB]')
plt.xlabel('angle [deg]')
plt.tight_layout()
plt.show()
print('thata: %.3f, theta_hat: %.3f'%(90-theta, est.theta_hat()))
if __name__ == '__main__':
fs = 48000 # sampling frequency. [Hz]
c = 340 # wave speed. [m/sec]
d = 0.1 # width for mic. array. [m]
theta = 75 # 0~180 [deg]
N_fft = 2048
simu_csp(theta=theta, fs=fs, N_fft=N_fft, c=c, d=d)
simu_music(theta=theta, fs=fs, N_fft=N_fft, c=c, d=d, N_theta=180+1)