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I'm trying to estimate PSD of a Binary signal with AWGN. Two inbuilt methods in MATLAB are giving me results one is Periodogram(Welch) and other is FFT squared. what is the basic difference between the two for giving me diffrent results? And which one is better please suggest.

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  • $\begingroup$ This is too broad. Both functions come with excellent documentation. Please state what of that you didn't understand. Hint: methods are almost never universally "better", unless you specify the specific measure for "good"ness. $\endgroup$ – Marcus Müller Dec 2 at 11:58
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Periodogram is an DTFT / FFT based nonparametric PSD estimator which is computed in Matlab/Octave by the following: $$ \hat{S}[k] = \frac{1}{N} |X[k]|^2 $$

Where $L$ is the length of the signal $x[n]$. It has got a number of options, including different windows, instead of a rectangular, to use.

Welch method is a variation of periodogram method in that it divides the signal $x[n]$ into smaller overlapping chunks, computes ordinary periodogram over those chuncks and then averages them to get the Welch estimate of PSD.

As you can see both methods depend on a squaring of DTFT / FFT however periodogram applies a raw FFT squaring whereas Welch applies an averaged FFT squaring method.

Welch's method will have less spectral resoluion but also less variance yielding a smoother, more reliable, estimate than the pure periodogram.

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  • $\begingroup$ Thanks for the detailed explanation. That clarified a lot. But i am asking clarification for the inbuilt simulink blocks of periodogram and |FFT|^2. because in MATLAB simulink periodogram is mentioned as periodogram (welch). $\endgroup$ – Gagan Singla Dec 4 at 6:08
  • $\begingroup$ ok actually the same answer... |FFT|^2 corresponds to bare Periodogram without overlapping averaging, whereas Periodogram(Welch) is an overlapped averaged version of bare Periodogram... What else can be said ? $\endgroup$ – Fat32 Dec 4 at 12:35

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