Periodogram of a square wave

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Gianmarco Lavacca
Gianmarco Lavacca on 30 May 2023
Commented: Gianmarco Lavacca on 11 Sep 2023 at 18:35
Hi everyone, I'm doing a DSP project where I need to extract the THD and SNDR of a Sigma-Delta DPWM.
I'm using the MATLAB function "periodogram" on the output to do it, but it returns bad results because the output wave is a square wave and not a sine wave (which amplifies the error). How can I work around that and get the correct periodogram of a square wave?
Thank you very much!
Gianmarco Lavacca
Gianmarco Lavacca on 31 May 2023
Edited: Gianmarco Lavacca on 31 May 2023
I don't really have the time to do that, the deadline is fairly near. I'll just own up to it in the report. Thank you very much for your help though. I'll leave the question open in case someone has suggestions.

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Accepted Answer

akshatsood on 4 Sep 2023 at 6:55
Edited: akshatsood on 6 Sep 2023 at 14:22
Hi Gianmarco,
I understand that you working on a Sigma-Delta DPWM. As stated in the question, you have used periodogram on the output square wave, yet it renders bad results. As per my understanding, you can leverage the fft function to compute the Fourier transform of the square wave and then calculate the power spectral density from the Fourier coefficients.
I have assumed a random data to discuss the workaround. Here is the code snippet for you reference
frequency = 10;
duration = 1;
samplingRate = 1000;
% generating square wave
t = 0:(1/samplingRate):(duration-1/samplingRate);
squareWave = square(2*pi*frequency*t);
N = length(squareWave);
Y = fft(squareWave); % computing Fourier transform
% determinging the power spectral density (PSD)
psd = (abs(Y).^2)/N;
f = samplingRate*(0:(N/2))/N; % frequency vector
% plot the square wave and the periodogram
title('Square Wave');
grid on;
plot(f, 10*log10(psd(1:N/2+1)));
xlabel('Frequency (Hz)');
ylabel('Power Spectral Density (dB/Hz)');
title('Periodogram of Square Wave');
grid on;
I believe that, following this approach would be helpful in supressing the errors and acheiving a satisfactory result for the periodogram of the square wave.
Have a look at the documentation page for fft function for better understanding
I hope this helps.
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Gianmarco Lavacca
Gianmarco Lavacca on 11 Sep 2023 at 18:35
Thank you very much. The exam is done and gone, but i'm sure your answer will help somebody else.

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