MATLAB: Generation of 1/f noise using Matlab.

1/f noise

Dear Colleagues, I have been trying to generate the 1/f noise, where f means frequency. I would appreciate any help and guidance. Kind regards,
Massilon

Best Answer

Probably the easiest way is to create a FIR filter that has a ‘1/f’ passband, then filter random noise through it:
fv = linspace(0, 1, 20);                                % Normalised Frequencies
a = 1./(1 + fv*2);                                      % Amplitudes Of ‘1/f’
b = firls(42, fv, a);                                   % Filter Numerator Coefficients
figure(1)
freqz(b, 1, 2^17)                                       % Filter Bode Plot
N = 1E+6;
ns = rand(1, N);
invfn = filtfilt(b, 1, ns);                             % Create ‘1/f’ Noise
figure(2)
plot([0:N-1], invfn)                                    % Plot Noise In Time Domain
grid
FTn = fft(invfn-mean(invfn))/N;                         % Fourier Transform
figure(3)
plot([0:N/2], abs(FTn(1:N/2+1))*2)                      % Plot Fourier Transform Of Noise
grid
It uses the firls function to design a FIR filter that closely matches the ‘1/f’ passband. See the documentation on the various functions to get the result you want.
Note: The filter is normalised on the open interval (0,1), corresponding to (0,Fn) where ‘Fn’ is the Nyquist frequency, or half your sampling frequency. It should work for any sampling frequency that you want to use with it.
This should get you started. Experiment to get the result you want.
Related Question