Generation of 1/f noise using Matlab.
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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
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Star Strider
2017년 6월 14일
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.
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Antonio D'Amico
2020년 8월 26일
Hello, thank you for your answer. If I understand the script correctly, it applies a 1/f (approximation) roll-off factor to the noise, whether it is uniformilly distributed (rand) or gaussian (randn). However what I would like to achieve is something like (From Wikimedia Commons)
![(From Wikimedia Commons)](https://www.mathworks.com/matlabcentral/answers/uploaded_files/351710/(From%20Wikimedia%20Commons).png)
I hope I was clearer
Antonio D'Amico
2020년 8월 26일
편집: Antonio D'Amico
2020년 8월 26일
Ok, I think I got it, something like this could work
fv = linspace(0, 1, 20); % Normalised Frequencies
a = zeros(1,20);
a(1:10) = 1./(1 + fv(1:10)*2); % Amplitudes Of 1/fv until 0.5
a(11:20) = a(10); % after 0.5 it gets flat
b = firls(42, fv, a); % Filter Numerator Coefficients
figure(1)
freqz(b, 1, 2^17) % Filter Bode Plot
N = 1E+6;
ns = randn(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
추가 답변 (2개)
Ali Mostafa
2018년 6월 11일
f=0:1/fs:1-1/fs;S=1./sqrt(f); S(end/2+2:end)=fliplr(S(2:end/2)); S=S.*exp(j*2*pi*rand(size(f))); plot(abs(S)) S(1)=0;figure;plot(real(ifft(S)))
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Massimo Ciacci
2019년 8월 10일
Quite ingenious to put the randomness in the phase, and this way the amplitude profile is exact, without the need to average out a lot of noise realizations. Thumbs up!
James
2023년 10월 3일
Hi were does 1./(1 + fv*2) come from?
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James
2023년 10월 3일
is there any paper or book I could look at to undestand that a bit more, or is this based on your own experience/skill?
Thank you very much for your response!
Star Strider
2023년 10월 3일
It’s entirely my own experience. I remember learning about
noise in graduate school, in the context of biomedical instrumentation. I’m certain there must be more recent discussions of it, however I have no specific references.
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1500835/image.png)
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