Plot autocorrelation and power spectrum

Hi..i'm a beginner in using Matlab. I'm currently trying to generate a Gaussian random numbers, then use it as an input to a low pass filter, cut-off frequency 1000Hz. I have the random number generated as: : f = randn(1000,1) * sqrt(2) + 0; I'd like to ask how can i proceed from here to calculate and plot the autocorrelation and power spectrum at input/output of the filter.

Answer 1

[Wayne King]

If you have the Signal Processing Toolbox, simply use xcorr() and periodogram()

   x = sqrt(2)*randn(1000,1);
   Numlags = 50;
   [xc,lags] = xcorr(x,Numlags,'coeff');
   stem(lags(51:end),xc(51:end))
   % power spectrum
   Fs = 1; % sampling frequency
   [Pxx,F] = periodogram(x,[],length(x),Fs);
   figure;
   plot(F,10*log10(Pxx))

[Aik Hong]

Thanks a lot ya~ Let me try it out then.

[Aik Hong]

Hi Wayne, btw, how can i implement this to a filter? example if i want to use the random number to a low pass filter with 1000Hz cutoff freq?

[Wayne King]

You need more information than that. You need to know minimally the sampling frequency.

[Aik Hong]

Oh ok. I've previously designed (in fdatool) the filter as the IIR Butterworth filter, sampling frequency 8000Hz and cutoff frequency 1000Hz. I've exported the filter to workspace.Can you advice me how should i use the random number generated as input to this filter and then plot its output autocorrelation and power spectrum?

Answer 2

[Wayne King]

It depends on what you have exported. If you exported a filter object -- I'll assume this.

Let Hd be your filter object

   x = randn(1000,1); % white noise input 1,000 samples in length
   y = filter(Hd,x);

[Aik Hong]

Thanks a lot. I got my output for autocorrelation and power spectrum like this: