Pink noise with specific power P

I need to generate pink noise signal with a specific power P. I can't figure it out on how to do that using the built-in function. Any help?

Answer 1

[Star Strider]

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

vp_pn1 = 0.0014

P = 25;                                         % Desired Pink Noise Power

k = sqrt(P / vp_pn1)                            % Scaling Constant

k = 134.7294

pn2 = pn1 * k;                                  % Scaled Pink Noise Vector

vp_pn2 = vp(pn2)                                % Mean Power Of Scaled Pink Noise Mean Power

vp_pn2 = 25

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')

y = 73113×1

0 -0.0062 -0.0750 -0.0312 0.0061 0.0381 0.0188 -0.0250 -0.0312 -0.0750

Fs = 8192

pn = pinknoise(numel(y))

pn = 73113×1

0.0466 0.0362 0.0269 0.0161 -0.0034 -0.0041 -0.0083 -0.0236 -0.0429 -0.0226

NewVector2 = @(OriginalSound,OriginalVector) sqrt(mean(OriginalSound.^2) ./ mean(OriginalVector.^2)) * OriginalVector;

Power_pn = mean(pn.^2)

Power_pn = 0.0011

Power_OriginalSound = mean(y.^2)

Power_OriginalSound = 0.0385

Power_NewVector = mean(NewVector2(y,pn).^2)                 % The Original 'pinknoise' Vector Now Has The Same Power As The Tyh Vector

Power_NewVector = 0.0385

.