pinknoise

Generate pink noise

Syntax

X = pinknoise(n)

X = pinknoise(sz1,sz2)

X = pinknoise(sz)

X = pinknoise(___,typename)

X = pinknoise(___,'like',p)

Description

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

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

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.

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

Examples

Generate Pink Noise

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

Amplitude Distribution of Pink Noise

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

Generate Multiple Independent Channels of Pink Noise

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)

Add Pink Noise to Audio Signal

Read in an audio file.

[audioIn,fs] = audioread("MainStreetOne-16-16-mono-12secs.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 = 
1.9791

noisePowerdB = 10*log10(noisePower)

noisePowerdB = 
-29.6665

signalPowerdB = 10*log10(signalPower)

signalPowerdB = 
-27.6874

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 = 
8

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

Input Arguments

n — Number of rows of pink noise

nonnegative integer

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

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

sz1,sz2 — Size of each dimension (as separate arguments)

nonnegative integers

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

sz — Size of each dimension (as a row vector)

one- or two-element row vector of nonnegative integers

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

typename — Data type to create

'double' (default) | 'single'

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

Data Types: char | string

p — Prototype of array to create

numeric array

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

X — Pink noise

column vector | matrix

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:

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

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Version History

Introduced in R2019b