# pinknoise

Generate pink noise

## Description

example

X = pinknoise(n) returns a pink noise column vector of length n.

example

X = pinknoise(sz1,sz2) returns a sz1-by-sz2 matrix. Each channel (column) of the output X is an independent pink noise signal.

example

X = pinknoise(sz) returns a vector or matrix with dimensions defined by the elements of vector sz. sz must be a one- or two-element row vector of positive integers. Each channel (column) of the output X is an independent pink noise signal.

X = pinknoise(___,typename) returns an array of pink noise of data type typename. The typename input can be either 'single' or 'double'. You can combine typename with any of the input arguments in the previous syntaxes.

example

X = pinknoise(___,'like',p) returns an array of pink noise like p. You can specify either typename or 'like', but not both.

## Examples

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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)

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)

## Input Arguments

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Number of rows of pink noise, specified as a nonnegative integer.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Size of each dimension, specified as a nonnegative integer or two separate arguments of nonnegative integers.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Size of each dimension, specified as a one- or two-element row vector of nonnegative integers. Each element of this vector indicates the size of the corresponding dimension.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Data type to create, specified as 'double' or 'single'.

Data Types: char | string

Prototype of array to create, specified as a numeric array. The generated pink noise is the same data type as p.

Data Types: single | double

## Output Arguments

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Pink noise, returned as a column vector or matrix of independent channels.

Data Types: single | double

## Tips

• The concatenation of multiple pink noise vectors does not result in pink noise. For streaming applications, use dsp.ColoredNoise.

## Algorithms

Pink noise is generated by passing uniformly distributed random numbers through a series of randomly initiated SOS filters. The resulting pink noise amplitude distribution is quasi-Gaussian and bounded between −1 and 1. The resulting pink noise power spectral density (PSD) is inversely proportional to frequency:

$S\left(f\right)\propto \frac{1}{f}$