fractalcoef

Filter coefficients for fractal noise generation

Since R2023b

Syntax

coeffs = fractalcoef

coeffs = fractalcoef(numPoles)

coeffs = fractalcoef(numPoles,alpha)

Description

coeffs = fractalcoef returns the filter coefficients for generating fractal noise with a power spectral density of 1/f, where f is the frequency. For more information on noise filtering, see filter.

Tip

You can use the generated coefficients to specify the BiasInstabilityCoefficients property of the accelparams, gyroparams, or magparams object.

coeffs = fractalcoef(numPoles) specifies the number of poles in the filter denominator coefficients.

coeffs = fractalcoef(numPoles,alpha) also specifies the alpha value (α) for the fractal noise with a power spectral density of 1/f ^α. When α = 1, the generated noise is also known as pink noise.

Examples

Generate Pink Noise and Obtain Allan Variance

First specify the frequency, number of samples, and number of poles for noise generation.

rng default % For repeatable results
Fs = 100;
numSamples = 2160000;
numPoles = 5;

Obtain filter coefficients using the fractalcoef function.

coeffs = fractalcoef(numPoles);

Generate white noise and filter the noise to obtain pink noise.

wn = randn(numSamples,1);
pn = filter(coeffs.Numerator,coeffs.Denominator,wn);

Generate Allan variance of the pink noise.

[avar,tau] = allanvar(pn,"octave",Fs);

Plot Allan deviation of the pink noise.

figure
adev = sqrt(avar);
loglog(tau, adev)
title("Allan Deviation of Pink Noise")
xlabel("\tau");
ylabel("\sigma(\tau)")
grid on
axis equal

Compare Fractal Noise for Various Values of Alpha

Define the number of samples, number of poles, and alpha values used to generate fractal noise.

rng default % For repeatable results
numSamples = 1e4;
numPoles = 1e3;
alphaValues = [0.1,0.5,1,1.5,1.9];

Create a series of white noise.

whiteNoise = randn(numSamples,1);

Generate fractal noise with different values of alpha using the fractalcoef and filter functions. Plot the generated fractal noise.

figure
for ii = 1:numel(alphaValues)
    coef = fractalcoef(numPoles,alphaValues(ii));
    fractalNoise = filter(coef.Numerator,coef.Denominator,whiteNoise);
    subplot(numel(alphaValues),1,ii)
    plot(fractalNoise)
    title("\alpha = " + num2str(alphaValues(ii)))
end

Input Arguments

numPoles — Number of poles

positive integer

Number of poles in the filter denominator coefficients, specified as a positive integer.

Example: 2

Data Types: single | double

alpha — Alpha value

1 (default) | scalar in range (0,2)

Alpha value (α), specified as a scalar in the range (0,2). The function returns the coefficients for generating fractal noise with a power spectral density of 1/f ^α.

Example: 0.9

Data Types: single | double

Output Arguments

coeffs — Coefficients for generating fractal noise

structure

Coefficients for generating fractal noise, returned as a structure. The structure has two fields:

• Numerator — Numerator of coefficients, returned as 1.

• Denominator — Denominator of coefficients, returned as a 1-by-(P+1) vector of scalars, where P is the number of poles.

References

[1] Kasdin, N. J. “Discrete Simulation of Colored Noise and Stochastic Processes and 1/f^α Power Law Noise Generation.” Proceedings of the IEEE, vol. 83, no. 5, May 1995, pp. 802–27.

Extended Capabilities

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

Version History

Introduced in R2023b