Generate 100 seconds of pink noise with a sample rate of 44.1 kHz.

fs = 44.1e3;
duration = 100;

y = pinknoise(duration*fs);

Plot the average power spectral density (PSD) of the generated pink noise.

[~,freqVec,~,psd] = spectrogram(y,round(0.05*fs),[],[],fs);
meanPSD = mean(psd,2);

semilogx(freqVec,db(meanPSD,"power"))
xlabel('Frequency (Hz)')
ylabel('PSD (dB/Hz)')
title('Power Spectral Density of Pink Noise (Averaged)')
grid on

Generate 500 seconds of pink noise with a sample rate of 16 kHz.

fs = 16e3;
duration = 500;

y = pinknoise(duration*fs);

Plot the relative probability of the pink noise amplitude. The amplitude is always bounded between $-$1 and 1.

histogram(y,"Normalization","probability","EdgeColor","none")
xlabel("Amplitude")
ylabel("Probability")
title("Relative Probability of Pink Noise Amplitude")
grid on

Create a 5 second stereo pink noise signal with a 48 kHz sample rate.

fs = 48e3;
duration = 5;
numChan = 2;

pn = pinknoise(duration*fs,numChan);

Listen to the stereo pink noise signal.

sound(pn,fs)

Channels of the pink noise function are generated independently. Note that the off-diagonal correlation coefficients are close to zero (uncorrelated).

R = corrcoef(pn(:,1),pn(:,2))

R = 2×2

    1.0000   -0.0190
   -0.0190    1.0000

Correlated and uncorrelated pink noise have different psychoacoustic effects. When the noise is correlated, the sound is less ambient and more centralized. To listen to correlated pink noise, send a single channel of the pink noise signal to your stereo device. The effect is most pronounced when using headphones.

sound([pn(:,1),pn(:,1)],fs)

Read in an audio file.

[audioIn,fs] = audioread("MainStreetOne-24-96-stereo-63secs.wav");

Create a pink noise signal of the same size and data type as audioIn.

noise = pinknoise(size(audioIn),'like',audioIn);

Add the pink noise to the audio signal and then listen to the first 5 seconds.

noisyMainStreet = noise + audioIn;
sound(noisyMainStreet(1:fs*5,:),fs)

The pinknoise function generates an approximate $-$29.5 dB signal level, which is close to the power of the audio signal.

noisePower = sum(noise.^2,1)/size(noise,1);
signalPower = sum(audioIn.^2,1)/size(audioIn,1);
snr = 10*log10(signalPower./noisePower)

snr = 1×2

   -0.3505   -1.6718

noisePowerdB = 10*log10(noisePower)

noisePowerdB = 1×2

  -29.6072  -29.5546

signalPowerdB = 10*log10(signalPower)

signalPowerdB = 1×2

  -29.9577  -31.2264

Mix the input audio with the generated pink noise at an 8 dB SNR.

desiredSNR = 8;
scaleFactor = sqrt(signalPower./(noisePower*(10^(desiredSNR/10))));

noise = noise.*scaleFactor;

Verify the resulting SNR is 8 dB and then listen to the first 5 seconds.

noisePower = sum(noise.^2,1)/size(noise,1);
snr = 10*log10(signalPower./noisePower)

snr = 1×2

    8.0000    8.0000

noisyMainStreet = noise + audioIn;
sound(noisyMainStreet(1:fs*5,:),fs)