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An input signal + (thermal) noise travels through a channel and can be measured at its output.

Is it possible to use cross correlation between input and output signal to measure group delay? If not, is there a better way to do this?

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You can use the cross correlation to measure the time delay between a signal and a delayed version of itself.

You can use cross correlation to estimate the transfer function.

You probably would benefit the most from PHAT

https://www.mathworks.com/matlabcentral/fileexchange/26256-calculate-ambiguity-function-and-utilities?focused=5143816&tab=function

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  • $\begingroup$ you mean GCC-PHAT, right? this does't look bad at all. I need more time to understand it. But as I am skimming through the topic, I was just wondering if it would give me the time delay per "frequency". As you may well know, the group delay, shows the delay of different frequency components of the signal. I like to have a graph representation of the signal, that shows me frequency on x-axis and time delay on y-axis, whereas I was hoping to suppress the of uncorrelated stuff (noise) in the process of cross correlation... $\endgroup$ – xaratustra Jun 15 '18 at 16:44
  • $\begingroup$ you suppress incoherent noise by averaging. Cross correlation is one place where complex averaging can work. If the signal is noise like, stationary like, effectively covers the bandwidth of the channel, you can use cross correlation to get the transfer function. A text on System Id will cover more general cases. The answer to your question is: maybe $\endgroup$ – Stanley Pawlukiewicz Jun 15 '18 at 17:50

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