MATLAB: How to calculate and plot power spectral density of a white noise signal

fast fourier transformfftMATLABpower spectrum densitypsdwhite noise

I want to ultimately find out how many bits are necessary to quantify noise of a signal. I'm working with this source code to generate a noisy white signal, and I know that taking the FFT to find the power spectral density (PSD) will allow me to then quantify voltage noise in the signal per rtHz or noise power per Hz.

When I run the code, I end up getting plots that look like this:

I've never worked with FFTs or PSDs before, and I'm only looking into them to answer my main question of how many bits I need to quantify a noise signal. As a result, I don't know how to discern what my PSD is by looking at these graphs. Is it the bandwidth? The average? I really am not sure.

Thanks.

Best Answer

Hi Sean,

The Power spectral density of a signal gives the Signal Power for the (at each) frequencies over the band. Since you are modelling a white noise for a specified bandwidth (by the ‘bandwidth’ variable), you get a nearly flat Absolute Noise power (the power shown in figure is reported in dB) over the band.

To quantify the number of bits required, you can use the dynamic range of the ‘noise’ variable to get the approximate estimate.

Hope this Helps.

Kiran Felix Robert

Related Solutions

MATLAB: Have a “Band Limited” White Noise Generator block instead of just a White Noise Generator block

Before this block was created, "White Noise" was being fed into CONTINUOUS-time blocks. The

resulting answer was not agreeing with what theory predicted.

The theory relates the Power Spectral Densities and the Transfer Function:

   PSD_Output(w) = TransferFunctionMagSquared(w) * PSD_Input(w)

Keep in mind that this analysis is in the continuous-time domain.

Passing ideal white noise through a zero-order-hold creates a stair-case signal with random tread heights. When viewed from the continuous-time domain, the PSD of this random stair-case is very different from that of ideal white noise. The ideal white noise will have a flat PSD:

   PSD_ideal_white(w) = P     % same value for all w

The exact same white noise passed through a zero-order-hold will have PSD

    PSD_staircase_white =  P * Tsamp * ( sinc( w * Tsamp ) )^2

Not only does the PSD falloff at higher frequencies with the behavior of sinc() squared, it also has a different value a DC frequency, namely P * Tsamp instead of P.

The Band-Limited White-Noise block restores the low frequency amplitude of the PSD by multiplying the individual samples by 1/sqrt(Tsamp). As a result, the Band-Limited White-Noise block will have PSD:

    PSD_bandlimited_white =  P * ( sinc( w * Tsamp ) )^2

At sufficiently low frequencies, the PSD is approximately

    PSD_bandlimited_white =  P   % w sufficiently small

so the Band-Limited-White-Noise will seem like ideal white noise to continuous-time blocks at these sufficiently low frequencies.

MATLAB: Calculate the frequency where psd is maximun

Hi, one thing you can do is to obtain a periodogram and then calculate the average power in an interval around the maximum frequency and then compare that to the average power from 0 to the Nyquist.

   Fs = 1e3;
   t = 0:1/Fs:1-(1/Fs);
   x = cos(2*pi*100*t)+randn(size(t));
   psdest = psd(spectrum.periodogram,x,'Fs',1e3,'NFFT',length(x));
   [mx,I] = max(psdest.Data);
    relperc = ...
    100*avgpower(psdest,[psdest.Frequencies(I-2) psdest.Frequencies(I+2)])/avgpower(psdest,[0 Fs/2])

Wayne

Best Answer

Related Solutions

MATLAB: Have a “Band Limited” White Noise Generator block instead of just a White Noise Generator block

MATLAB: Calculate the frequency where psd is maximun

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