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I need to find a time delay between the two audio signals, one comming from one set of speakers, and the other being the source signal that is initialy sent to speakers. I send some noise through those speakers and they come to microphone with a time delay compared to a source signal.

Cross-correlation method
As I understand, there is a cross-correlation method where I send both recorded signals to frequency domain via Discrete Fourier Transform (DFT), then multiply the frequencies, and finaly go back to time domain via Inverse DFT. There should be a peak in time domain telling me what the delay is (let's disregard the accuracy for now.)

IR method
There is also an Impulse Response method, where I also take two signals to freq domain via DFT, then divide the two to get a system transfer function, and finaly do an Inverse DFT of the Transfer function; this will give me the Impulse Response, which should also have a strong peak at the delay point.

My question is:
Am I right in the short descriptions above? The main difference between the two methods seems to be that frequencies are multiplied in the cross-correletion method, and dividied in the IR method? Have I missed something important?

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  • $\begingroup$ I think it also depends a bit on what the audio signals are and if there is only a delay between the input and output or it's more complex response $\endgroup$ – Cherny Oct 9 '17 at 13:27
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Your description of the cross-correlation method is not entirely correct. What you describe is actually a convolution. For a cross-correlation you would perform an FFT on both signals and then multiply one with the complex conjugate of the other, and finally perform an IFFT.

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    $\begingroup$ you're describing an implementation of the cross-correlation not cross-correlation itself. A cross-correlation is pretty much the same as convolutioning a signal with itself without time reversal. $\endgroup$ – Ben Dec 8 '17 at 19:48

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