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My question is that when I used gcc-phat to estimate delay between two audio signals, it always returns zero offset. However normal cross correlation Xcorr gives a good result. I don't know the reason.

It is the same case as below two:

GCC-PHAT (Generalized cross correlation MATLAB)

GCC-PHAT (Generalized cross correlation) always peak at delay=0 on real audio signal

I have tried to remove the DC part of signals but it doesn't work. Any suggestion is appreciated!

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This code seems to work (included also below).

Pythonizing the first example link you include seems to do the right thing with that code.

Fs = 8000
dt = 1/Fs #0.125e-3
f1 = 100
tdelay = 0.625e-03 # try different values
t3 = np.linspace(0.0,1.0,Fs)
x3 = np.cos(2*np.pi*f1*t3);
x4 = np.cos(2*np.pi*f1*(t3-tdelay));
gcc_phat(x4,x3)

yields:

(0.375, array([-0.02514735, -0.02196879, -0.01847165, ..., -0.0303065 , -0.02794452, -0.02514735]))

(which gives one minus the actual delay).

After playing with your wav file (thanks!), I think the problem is that your recording equipment has too much correlated noise across all four channels. That's giving a GCC-PHAT peak at zero.

If I try to drown out the noise by adding even more (uncorrelated) noise, then I get a better result: -5 samples vs -4 samples from XCORR.

Results with added noise.

The four plots are:

  1. The section of one channel that I'm looking at.

  2. The GCC-PHAT central part when uncorrelated Gaussian noise is added to the data.

  3. The GCC-PHAT central part when no noise is added to the data.

  4. The XCORR result of the noiseless data.

Code to do this is below and on GitHub. I originally though it might be possible to just filter the data, but that doesn't help at all.

import numpy as np
import statistics
from scipy.io import wavfile
import matplotlib.pyplot as plt
from IPython.display import Audio
from scipy.signal import kaiserord, lfilter, firwin, freqz


samplerate, data = wavfile.read("Q69905.wav",'rb')
samples = np.arange(20000,30000)

fir_filter = firwin(123,0.75)
channel_1 = lfilter(fir_filter,1, data[samples,0])
channel_2 = lfilter(fir_filter,1, data[samples,1])
channel_3 = lfilter(fir_filter,1, data[samples,2])
channel_4 = lfilter(fir_filter,1, data[samples,3])

noise_1 = np.random.normal(0,1000,len(channel_1))
noise_2 = np.random.normal(0,1000,len(channel_2))
noise_3 = np.random.normal(0,1000,len(channel_3))
noise_4 = np.random.normal(0,1000,len(channel_4))

print([statistics.mean(data[:,0]),  statistics.mean(data[:,1]), statistics.mean(data[:,2]), statistics.mean(data[:,3])])

# delay, gcc = gcc_phat(data[samples,0].astype(float)+10, data[samples,2].astype(float)+12, interp=1)
delay, gcc = gcc_phat(channel_1 + noise_1, channel_3 + noise_3, interp=1)
delay_no_noise, gcc_no_noise = gcc_phat(channel_1 , channel_3 , interp=1)

plt.figure(figsize=(20,30))
plt.subplot(4, 1, 1)
plt.plot(data[samples,0])
plt.subplot(4, 1, 2)
plt.plot(np.arange(-10,10),gcc[9990:10010],'.') # [9950:10050]
plt.subplot(4, 1, 3)
plt.plot(np.arange(-10,10),gcc_no_noise[9990:10010],'.') # [9950:10050]
plt.subplot(4, 1, 4)
lags,c, line, b = plt.xcorr(channel_1,channel_3)
plt.plot(lags,c,color='r')

print('GCC-PHAT: ' + str(delay))
print('XCORR: ' +  str(lags[np.argmax(c)]))
Audio(channel_1 + noise_1, rate=44100)

Code From GitHub

"""
 Estimate time delay using GCC-PHAT 
 Copyright (c) 2017 Yihui Xiong
 Licensed under the Apache License, Version 2.0 (the "License");
 you may not use this file except in compliance with the License.
 You may obtain a copy of the License at
     http://www.apache.org/licenses/LICENSE-2.0
 Unless required by applicable law or agreed to in writing, software
 distributed under the License is distributed on an "AS IS" BASIS,
 WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 See the License for the specific language governing permissions and
 limitations under the License.
"""

import numpy as np


def gcc_phat(sig, refsig, fs=1, max_tau=None, interp=16):
    '''
    This function computes the offset between the signal sig and the reference signal refsig
    using the Generalized Cross Correlation - Phase Transform (GCC-PHAT)method.
    '''
    
    # make sure the length for the FFT is larger or equal than len(sig) + len(refsig)
    n = sig.shape[0] + refsig.shape[0]

    # Generalized Cross Correlation Phase Transform
    SIG = np.fft.rfft(sig, n=n)
    REFSIG = np.fft.rfft(refsig, n=n)
    R = SIG * np.conj(REFSIG)

    cc = np.fft.irfft(R / np.abs(R), n=(interp * n))

    max_shift = int(interp * n / 2)
    if max_tau:
        max_shift = np.minimum(int(interp * fs * max_tau), max_shift)

    cc = np.concatenate((cc[-max_shift:], cc[:max_shift+1]))

    # find max cross correlation index
    shift = np.argmax(np.abs(cc)) - max_shift

    tau = shift / float(interp * fs)
    
    return tau, cc


def main():
    
    refsig = np.linspace(1, 10, 10)

    for i in range(0, 10):
        sig = np.concatenate((np.linspace(0, 0, i), refsig, np.linspace(0, 0, 10 - i)))
        offset, _ = gcc_phat(sig, refsig)
        print(offset)


if __name__ == "__main__":
    main()
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    $\begingroup$ Hi Peter, thanks for your answer. I have tried this code with my audio files, but it also failed...I uploaded my audio file (4 channels totally) here. The delay between channel 1 and channel 3 is -4 with xcorr, but 0 with the code in your answer. Could you please have a look at what happened? $\endgroup$ – Qiang Aug 21 at 14:50
  • $\begingroup$ @Qiang OK! I'll see if I can run it on that data. Probably not soon, but later this evening (my time). Thanks for the data. $\endgroup$ – Peter K. Aug 21 at 14:56
  • $\begingroup$ That's okay! Take your time. looking forward to your insight! $\endgroup$ – Qiang Aug 21 at 15:17
  • $\begingroup$ @Qiang OK. See my update. $\endgroup$ – Peter K. Aug 21 at 16:52
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    $\begingroup$ Thanks for your feedback! I also considered filtering signals but doesn't work. Maybe it is indeed caused by the hardware correlated noise. I will keep on searching for the solution. Anyway, thanks for your help again! $\endgroup$ – Qiang Aug 22 at 13:45

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