# Equivalence of Maximum Likelihood (ML) and Discrete Fourier Transfrom (DFT) Peak Finding for Single Tone Estimation

My understanding is Maximum Likelihood and DFT Peak Finding for a single tone produce the same results assuming the ML is restricted to the same frequencies as the DFT.

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 DFT peak gives the best Least Squares estimate of single tone sinusoidal.

• 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? – FourierFlux Feb 9 '19 at 20:30
• yea sometimes I forget. – FourierFlux Jun 27 '19 at 7:02