MATLAB: To generate a random signal with the given PSD

MATLABpsdrandom signalsimulink

How to generate a random signal with the given PSD and upper and lower cut-off frequencies in MATLAB or SIMULINK? Whether possible or not?

Best Answer

Normally this is done by generating a filter according to the given PSD and then pass a white noise through the filter.

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: How to generate band-limited Gaussian white noise?

You cannot generate band-limited "white" Gaussian noise. "White" noise means that the power spectral density is flat, which contradicts the notion of a passband.

You can generate band-limited Gaussian noise. I'm not sure what you mean by "...signal ranging from 0 to 3 with a frequency of 0-6Hz", so I'll assume that you want a passband of 0 to 6 Hz. You did not tell us your sampling frequency, I'll assume 100 Hz.

      Fs = 100;
      d = fdesign.lowpass('Fp,Fst,Ap,Ast',6,10,0.5,40,Fs);
      B = design(d);
      % create white Gaussian noise the length of your signal
      x = randn(1000,1);
      % create the band-limited Gaussian noise
      y = filter(B,x);

The output, y, is a band-limited Gaussian noise with a passband of 0 to 6 Hz.

Best Answer

Related Solutions

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

MATLAB: How to generate band-limited Gaussian white noise?

Related Question