For microphone arrays ,N Whether there is a delay between microphones , Can pass N The phase difference between data . Phase difference is one of the important indicators to judge the synchronization of microphone signal .
First, explain what is phase and phase difference .
phase (phase) It's for a wave , The position of a particular moment in its cycle ： Whether it's on the crest 、 The scale of a trough or a point between them .
Phase describes the measurement of signal waveform change , Usually, the degree （ angle ） As a unit , Also called phase angle . When the signal waveform changes periodically , The waveform circulates for one cycle 360° .
for example ： In function y=Acos(ωx+φ) in ,ωx+φ be called phase .
Phase difference ： The difference between the phases of two physical quantities that change periodically with the same frequency is called the phase difference , Or difference .
Phase difference in simple harmonic motion ： If the frequencies of two simple harmonic motions are equal , The initial phases are φ1,φ2. When φ2>φ1 when , Their phase difference is ：
△φ=(ωt+φ2)-(ωt+φ1)=φ2-φ1
At this time we often say 2 Phase ratio of 1 leading △φ.
The following mainly talks about how to use python Find the phase difference between microphone array signals . Take two signals for example , Suppose the two signals are data obtained from two microphone signals .
The signal in the recorded audio is a time domain signal , It needs to be transformed into frequency domain signal by Fourier transform , The data after Fourier transform is complex , The real part is the amplitude , The imaginary part represents the phase . The most important step in phase calculation is Unwinding .
Specific explanation of unwinding , Please refer to the following link ：
https://blog.csdn.net/bpssy/article/details/22218589
Libraries to be called ：
import wave
import numpy as np
import scipy.signal as signal
import matplotlib.pyplot as plt
Set the sampling rate and duration ：
framerate = 16000
time = 1
Generate two signals , The phase difference between the two signals is 10°：
# Generation duration 1 Second sampling rate 16kHz Of 100Hz - 8kHz Frequency sweep signal
t = np.arange(0, time, 1.0/framerate)
wave_data = signal.chirp(t, 100, time, 8000, method='linear')
wave_data2 = signal.chirp(t, 100, time, 8000, method='linear',phi = 10)
Carry out Fourier transform , Time domain variable frequency domain ：
data1 = np.fft.rfft(wave_data)/len(wave_data)
fr = np.fft.rfftfreq(len(wave_data),1/framerate)
sp1 = 20*np.log10(np.abs(data1))
data11 = np.fft.fft(wave_data)
data21 = np.fft.fft(wave_data2)
data111 = np.angle(data11, deg = True)
data211 = np.angle(data21,deg = True)
# Unwind the data unwrap#
data112 = data111/180*np.pi
data113 = np.unwrap(data112)
mapping , Show results ：
plt.figure('Phase_delta',figsize=(8,4))
plt.plot((data213[:512]-data113[:512])*180/np.pi,label = 'data213-data113')
plt.ylim(0,50)
plt.legend()
plt.show()
The final result is as follows , The phase difference between the effective frequency intervals of the two signals is 10 degree , In line with expectations .
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