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Can anyone explain why autocorrelation can be more efficiently calculated using the fft ?

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Bcause the FFT is computed usingn $N\log N$ arithmetic operations, whereas the DFT using $N^2$ operations, where $N$ is the number of points in your discrete-time signal. So the number of operations is much lower if $N$ is particularly high, which is often the case ...

Watch this video if you want to know more about this https://www.youtube.com/watch?v=iTMn0Kt18tg

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  • $\begingroup$ you've compared FFT to DFT, I would suggest for better understanding of readers instead of DFT refer to autocorrelation itself. $\endgroup$ – MimSaad Aug 6 at 0:59

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