# Periodogram and Welch periodogram comparison

I'm trying to compute the PSD using the periodogram method. I have a signal that is periodical at 5kHz. The frequency resolution sought for is 1.221Hz. It's a PRBS signal that has its energy drop to zero at the generation frequency, i.e. 5kHz in this case. The signals i prety much noise clean.

I tried computing the periodogram and I get what I'm after. Then I tried using Welch's averaging method with N = 500 segment length and overlap of 50% and I get something completely different. I would expect to see an exact copy of the periodogram since there is practicaly no noise. Did I completely misunderstood the method?

What I obtain is this:

I used the following lines of code to estimate the periodogram exactly at the frequencies I want and I scaled the periodogram. ( I have also added .mat files if anyone wants to give it a go)

load('data.mat');
1/DT = 5000;
[pxxp,fp] = periodogram(V,rectwin(length(V)),freq,1/DT);
[pxxw,fw] = pwelch(V,rectwin(500),250,freq,1/DT);

semilogx(fp,20*log10(pxxp*8775))
hold on
semilogx(fw,20*log10(pxxw))

• What is the length of the input?
– user28715
Commented Jan 17, 2019 at 14:05
• 131040 samples. Commented Jan 17, 2019 at 14:07
• In one case you average and the other you do not. Why expect the same?
– user28715
Commented Jan 17, 2019 at 14:11
• Use the same window length of you expect to see the same result
– user28715
Commented Jan 17, 2019 at 14:26
• Because I would at least expect to see something similar like here: commons.wikimedia.org/wiki/… I also tried with another signal that has some noise inside and the periodograms are really off... Commented Jan 17, 2019 at 14:42

Looks similar to me

>  clear all
>     close all