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Spectrum of discrete-time random process - DFT of autocorrelation, vs signal itself

Started by dsavio 4 years ago3 replieslatest reply 4 years ago89 views

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Reply by kazJune 28, 2018

TRUE spectrum is obtained if you arrange a bank of many filters each passing one bin brick wall then compute power. I don't see what correlation is going to offer.

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Reply by GregLapinJune 28, 2018

It seems to me that by performing the autocorrelation you are doubling your time domain data, which is then transformed to the frequency domain.  However, you aren't creating more time domain data, just a copy of the original set.  Even though your frequency domain has twice the samples they do not add any frequency resolution.  Rather, it is similar to interpolating between the original frequency samples, which is also what you get when you zero-pad the time domain data.

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Reply by jbrowerJune 28, 2018

Dsavio-

My comment is in the spirit of the time-worn saying "if something looks too good to be true, then it probably is".  During the process you describe, time domain resolution (i.e. sampling rate) has not been increased, so there is no new information you can transform into the frequency domain.  You can always do larger and larger FFTs (applying zero padding), which would let you look at increasingly narrow bins, but mathematically, you would not "uncover" new data.

-Jeff