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My understanding is Maximum Likelihood and FFT peak finding for a single tone produce the same results assuming the ML is restricted to the same frequencies as the FFT.

I was wondering if there was an easy way to prove this? My understanding is that ML will be the same doing least-squares regression so I suppose an equivalent statement would be to prove that the FFT peak gives the best least squares estimate of single-tone sinusoid.

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  • $\begingroup$ I think I figured it out: DFT applies a correlation, choosing the strongest correlation(peak detection) gives the best estimate using the difference squared norm which is equivalent to minimizing the sum in joint PDF for uncorrelated gaussians. Am I wrong? $\endgroup$ – FourierFlux Feb 9 at 20:30

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