# Generate pinknoise with same power as audio

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L am 25 Aug. 2023
Beantwortet: Mathieu NOE am 28 Aug. 2023
I need to read an audio file and generate a pinknoise with the same power.
I tought using generatepinknoise(), but the built-in function does not accept a power specification.
Any ideas?
I was trying something based on https://stackoverflow.com/questions/17795675/making-pink-noise-1-f-using-list-of-frequencies, but it dosen't sound anything like pinknoise.
% Generate pinknoise with same power as sound
% get sound (2 channels)
Y=fft(y);
A1 = abs(Y(:,1)); P1 = mean(A1.^2);
A2 = abs(Y(:,2)); P2 = mean(A2.^2);
N = length(Y); invfnorm = 1./[1:N]';
Anew1 = sqrt(P(:,1)*invfnorm/sum(invfnorm)); Anew2 = sqrt(P(:,2)*invfnorm/sum(invfnorm));
noise = ifft([Anew1 .* exp(1i*angle(Y(:,1))) Anew1 .* exp(1i*angle(Y(:,1))) ] ,'symmetric');
soundsc(noise,Fs)
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### Akzeptierte Antwort

Mathieu NOE am 28 Aug. 2023
hello
this would be my suggestion . You don't need to do a fft to get the power of a signal (you can compute it directly in time domain too)
here I tested it on my own audio signal (piano.wav)
% Generate pinknoise with same power as sound
% get sound (2 channels)
% [y,Fs] = audioread('piano.wav'); % mine
[samples,channels] = size(y);
y_power = mean(y.^2,1); % power of signals
pn = mypinknoise(samples);
pn_power = mean(pn.^2); % yes it's 1 because normalized std as explained in the subfunction
% let's assume we want same pink noise power as audio channel of largest
% power
pow_factor = max(y_power)/pn_power;
% now the pink noise signal must be multiplied by the square root of the
% power factor
pn = pn*sqrt(pow_factor);
pn_power = mean(pn.^2); % double check ; now we have same noise power as the audio signal
% concatenate signals for replay
out = [y; pn(:)*ones(1,channels)];
soundsc(out,Fs);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function y = mypinknoise(N)
% function: y = pinknoise(N)
% N - number of samples to be returned in a row vector
% y - a row vector of pink (flicker) noise samples
% The function generates a sequence of pink (flicker) noise samples.
% In terms of power at a constant bandwidth, pink noise falls off at 3 dB/oct, i.e. 10 dB/dec.
% difine the length of the vector and
% ensure that the M is even, this will simplify the processing
if rem(N, 2)
M = N+1;
else
M = N;
end
% generate white noise
x = randn(1, M);
% FFT
X = fft(x);
% prepare a vector with frequency indexes
NumUniquePts = M/2 + 1; % number of the unique fft points
n = 1:NumUniquePts; % vector with frequency indexes
% manipulate the left half of the spectrum so the PSD
% is proportional to the frequency by a factor of 1/f,
% i.e. the amplitudes are proportional to 1/sqrt(f)
X = X(1:NumUniquePts);
X = X./sqrt(n);
% prepare the right half of the spectrum - a conjugate copy of the left one,
% except the DC component and the Nyquist component - they are unique
% and reconstruct the whole spectrum
X = [X conj(X(end-1:-1:2))];
% IFFT
y = real(ifft(X));
% ensure that the length of y is N
y = y(1, 1:N);
% ensure unity standard deviation and zero mean value
y = y - mean(y);
y = y/std(y, 1);
end
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