Create a scaling constant defined by:
k = sqrt(DesiredPower / ActualPower)
then multiply that by the original vector.
Equivalently:
newVector = sqrt(DesiredPower/mean(OriginalVector.^2)) * OriginalVector
The resulting vector has the desired power.
Try this —
vp = @(x) mean(x.^2); % Mean Power
n = 100;
pn1 = pinknoise(n); % Pink Noise Vector
vp_pn1 = vp(pn1) % Mean Power Of Pink Noise Vector
P = 25; % Desired Pink Noise Power
k = sqrt(P / vp_pn1) % Scaling Constant
pn2 = pn1 * k; % Scaled Pink Noise Vector
vp_pn2 = vp(pn2) % Mean Power Of Scaled Pink Noise Mean Power
figure
pspectrum(pn1)
title('Original')
figure
pspectrum(pn2)
title('Scaled')
EDIT — (28 August 2023 at 15:10)
To create pink noise with the same power as a particular signal, use a variation of this —
load handel.mat
filename = 'handel.wav';
audiowrite(filename,y,Fs);
clear y Fs
[y,Fs] = audioread('handel.wav')
pn = pinknoise(numel(y))
NewVector2 = @(OriginalSound,OriginalVector) sqrt(mean(OriginalSound.^2) ./ mean(OriginalVector.^2)) * OriginalVector;
Power_pn = mean(pn.^2)
Power_OriginalSound = mean(y.^2)
Power_NewVector = mean(NewVector2(y,pn).^2) % The Original 'pinknoise' Vector Now Has The Same Power As The Tyh Vector
.
