MATLAB: Band limited white noise

fftMATLABsignal processing

I need to make random excitation and I usually do that by "randn" command. However, I have to make random excitation with broadband frequency components, namely to excite certain frequencies. Let's say my sampling frequency (fs) is 50Hz and I need to have random white noise in range of 0 to 8 Hz to make sure this range is adequately excited.
I appreciate if someone gives me a simple way to do that which could be applied to general cases.
Cheers

Best Answer

Create a lowpass filter with the appropriate passband and then use the filtfilt function to filter your noise signal. The output should be band-limited noise that matches your specifications. If you need help in designing and implementing your filter, my filter design procedure is here: How to design a lowpass filter for ocean wave data in Matlab?
See if this works for you:
Fs = 5E+4;                                  % Sampling Frequency (Hz)
Fn = Fs/2;                                  % Nyquist Frequency (Hz)
Fco = 8;                                    % Cutoff Frequency (Hz)
Wp = Fco/Fn;                                % Normalised Cutoff Frequency (rad)
Ws = 1.6*Wp;                                % Stopband Frequency (rad)
Rp =  3;                                    % Passband Ripple (dB)
Rs = 20;                                    % Stopband Ripple (dB)
[n,Wn]  = buttord(Wp,Ws,Rp,Rs);             % Calculate Filter Order
[b,a]   = butter(n,Wn);                     % Calculate Filter Coefficients
[sos,g] = tf2sos(b,a);                      % Convert To Second Order Section Representation
figure(1)
freqz(sos, 1024, Fs)                        % Plot Filter Response (Bode Plot)
L = 1E+6;                                   % Signal Length
noise = randn(1, L);                        % White Noise
filtered_noise = filtfilt(sos,g,noise);     % Band-Limited Noise
FTfn = fft(filtered_noise)/L;               % Fourier Transform Of Filtered Signal
Fv = linspace(0, 1, fix(L/2)+1)*Fn;         % Frequency Vector
Iv = 1:length(Fv);                          % Index Vector
figure(2)
plot(Fv, abs(FTfn(Iv)))
axis([0  50    ylim])
grid
title('Band-Limited Noise')
xlabel('Frequency (Hz)')
ylabel('Amplitude')
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