# Power spectral density plot in terms of non dimensional frequency

I analyzed a voltage signal and plotted the PSD. However, I need to produce a power-spectral-density plot from the data in terms of non-dimensional frequency. How do I calculate the Strouhal number for the frequency range and generate an SPL plot for it?

nfft=2048;
window = hann(nfft);
overlap = 0;
[PSD, freq] = pwelch(det_data, window, overlap, nfft,fs);
figure;
plot(freq, 10*log10(PSD), 'b');
title('Power Spectral Density');
xlabel('Frequency (Hz)');
ylabel('Power Spectral Density (dB/Hz)');

• what's "non-dimensional frequency"? Commented Jun 3, 2023 at 11:11
• How do I calculate the Strouhal number for the frequency range and generate an SPL plot for it? Commented Jun 3, 2023 at 12:22
• That seems to be a separate question, or is it related? If it's a question, it should be in your question post, not a comment, S_saleem! Also, a "Strouhal number" is not a signal processing concept, as far as I know, so you need to define that term as well – or at least link to a good definition. Note that this is a platform full of signal processing expertise, but very few experts on fluid dynamics. Asking about something here thus probably only works if you can abstract your question from fluid dynamics into signal processing, or give us the formulas to help you do that! Commented Jun 3, 2023 at 12:34
• I have edited the question. Please have a look at it and let me know Commented Jun 3, 2023 at 12:44
• that edit defines neither "non-dimensional frequency" nor "Strouhal number", so I'm not sure it helps. Or is that "the frequency is, thus, defined as $\mathrm{St} = fD_j/U_j$" the definition of "non-dimensional frequency"? In that case, what are $D_j$ and $U_j$? Commented Jun 3, 2023 at 12:59

## 1 Answer

1.- To go from PSD to SPL

it seems from the screen shot in the question that to go from PSD to SPL all that has to be done is to apply the Pref factor

SPL=PSD-10*log10((20*1e-6)^2)

10*log10((20*1e-6)^2)
=
-93.9794


2.- St definition

From

https://www.engineeringtoolbox.com/strouhal-number-d_582.html

The Strouhal number St is defined as

St=w*L/v

L : Characteristic Length

v : Flow velocity

w : Oscillation frequency

Again

3.- Missing Data

One cannot tell whether w should be w=2*pi*f or one can readily replace with f in the St definition.

So far v and L seem unknown, but it may be the case that both can be inferred from the supplied graph.

It's also probable that f is referred to the peak frequency that is located on approximately 2600Hz on the supplied graph.

St As defined in the screenshot St=f*D(j)/U(j)

means that D is L the Characteristic Length and U is v the Flow Velocity.

Yet D and U seem to be vectors.

If only more details about the experiment were known, readers would be able to further assist.

Appreciating time and attention.

• "One cannot tell whether w should be w=2*pi*f" I know nothing of this topic but it really seems that the formula should read via $f$, not $\omega$, as latter introduces the radian dimension. This "controversial" unit often, if not most of the time, can't be neglected. I also just checked, Wiki uses $f$. OP's plots and formulae also use $f$. Commented Jun 5, 2023 at 13:24