Noise Processes

The stochastic.processes.noise module provides classes for generating noise processes.

Gaussian increments

Colored noise

Gaussian increments

Noise processes which are increments of their continuous counterparts.

class stochastic.processes.noise.GaussianNoise(t=1, rng=None)[source]

Gaussian noise process.

_images/gaussian_noise.png

Generate a sequence of Gaussian random variables.

Parameters

  • t (float) – the right hand endpoint of the time interval \([0,t]\) for the process

  • rng (numpy.random.Generator) – a custom random number generator

sample(n)[source]

Generate a realization of Gaussian noise.

Generate a Gaussian noise realization with n increments.

Parameters

n (int) – the number of increments to generate.

sample_at(times)[source]

Generate Gaussian noise increments at specified times from zero.

Parameters

times – a vector of increasing time values for which to generate noise increments.

property t

End time of the process.

times(n)

Generate times associated with n increments on [0, t].

Parameters

n (int) – the number of increments

class stochastic.processes.noise.FractionalGaussianNoise(hurst=0.5, t=1, rng=None)[source]

Fractional Gaussian noise process.

_images/fractional_gaussian_noise.png

Generate sequences of fractional Gaussian noise.

Hosking’s method:

  • Hosking, Jonathan RM. “Modeling persistence in hydrological time series using fractional differencing.” Water resources research 20, no. 12 (1984): 1898-1908.

Davies Harte method:

  • Davies, Robert B., and D. S. Harte. “Tests for Hurst effect.” Biometrika 74, no. 1 (1987): 95-101.

Parameters

  • hurst (float) – The Hurst parameter value in \((0,1)\).

  • t (float) – the right hand endpoint of the time interval \([0,t]\) for the process

  • rng (numpy.random.Generator) – a custom random number generator

property hurst

Hurst parameter.

sample(n, algorithm='daviesharte')[source]

Generate a realization of fractional Gaussian noise.

Parameters

  • n (int) – number of increments to generate

  • algorithm (str) – either ‘daviesharte’ or ‘hosking’ algorithms

property t

End time of the process.

times(n)

Generate times associated with n increments on [0, t].

Parameters

n (int) – the number of increments

Colored noise

Signals with spectral densities proportional to the power law.

class stochastic.processes.noise.BlueNoise(t=1, rng=None)[source]

Blue noise.

_images/blue_noise.png

Colored noise, or power law noise with spectral density exponent \(\beta = -1\).

Parameters

  • t (float) – the right hand endpoint of the time interval \([0,t]\) for the process

  • rng (numpy.random.Generator) – a custom random number generator

sample(n)

Generate a realization of colored noise.

Generate a colored noise realization with n increments.

Parameters

n (int) – the number of increments to generate.

property t

End time of the process.

times(n)

Generate times associated with n increments on [0, t].

Parameters

n (int) – the number of increments

class stochastic.processes.noise.BrownianNoise(t=1, rng=None)[source]

Brownian (red) noise.

_images/red_noise.png

Colored noise, or power law noise with spectral density exponent \(\beta = 2\).

Parameters

  • t (float) – the right hand endpoint of the time interval \([0,t]\) for the process

  • rng (numpy.random.Generator) – a custom random number generator

sample(n)

Generate a realization of colored noise.

Generate a colored noise realization with n increments.

Parameters

n (int) – the number of increments to generate.

property t

End time of the process.

times(n)

Generate times associated with n increments on [0, t].

Parameters

n (int) – the number of increments

class stochastic.processes.noise.ColoredNoise(beta=0, t=1, rng=None)[source]

Colored noise processes.

_images/colored_noise.png

Also referred to as power law noise, colored noise refers to noise processes with power law spectral density. That is, their spectral density per unit bandwidth is proportional to \((1/f)^\beta\), where \(f\) is frequency with exponent \(\beta\).

Uses the algorithm from:

  • Timmer, J., and M. Koenig. “On generating power law noise.” Astronomy and Astrophysics 300 (1995): 707.

Generates a normalized power-law spectral noise.

Parameters

  • beta (float) – the power law exponent for the spectral density, with 0 being white noise, 1 being pink noise, 2 being red noise (Brownian noise), -1 being blue noise, -2 being violet noise. Default is 0 (white noise).

  • t (float) – the right hand endpoint of the time interval \([0,t]\) for the process

  • rng (numpy.random.Generator) – a custom random number generator

property beta

Power law exponent.

sample(n)[source]

Generate a realization of colored noise.

Generate a colored noise realization with n increments.

Parameters

n (int) – the number of increments to generate.

property t

End time of the process.

times(n)

Generate times associated with n increments on [0, t].

Parameters

n (int) – the number of increments

class stochastic.processes.noise.RedNoise(t=1, rng=None)[source]

Red (Brownian) noise.

_images/red_noise.png

Colored noise, or power law noise with spectral density exponent \(\beta = 2\).

Parameters

  • t (float) – the right hand endpoint of the time interval \([0,t]\) for the process

  • rng (numpy.random.Generator) – a custom random number generator

sample(n)

Generate a realization of colored noise.

Generate a colored noise realization with n increments.

Parameters

n (int) – the number of increments to generate.

property t

End time of the process.

times(n)

Generate times associated with n increments on [0, t].

Parameters

n (int) – the number of increments

class stochastic.processes.noise.PinkNoise(t=1, rng=None)[source]

Pink (flicker) noise.

_images/pink_noise.png

Colored noise, or power law noise with spectral density exponent \(\beta = 1\).

Parameters

  • t (float) – the right hand endpoint of the time interval \([0,t]\) for the process

  • rng (numpy.random.Generator) – a custom random number generator

sample(n)

Generate a realization of colored noise.

Generate a colored noise realization with n increments.

Parameters

n (int) – the number of increments to generate.

property t

End time of the process.

times(n)

Generate times associated with n increments on [0, t].

Parameters

n (int) – the number of increments

class stochastic.processes.noise.VioletNoise(t=1, rng=None)[source]

Violet noise.

_images/violet_noise.png

Colored noise, or power law noise with spectral density exponent \(\beta = -2\).

Parameters

  • t (float) – the right hand endpoint of the time interval \([0,t]\) for the process

  • rng (numpy.random.Generator) – a custom random number generator

sample(n)

Generate a realization of colored noise.

Generate a colored noise realization with n increments.

Parameters

n (int) – the number of increments to generate.

property t

End time of the process.

times(n)

Generate times associated with n increments on [0, t].

Parameters

n (int) – the number of increments

class stochastic.processes.noise.WhiteNoise(t=1, rng=None)[source]

White noise.

_images/white_noise.png

Colored noise, or power law noise with spectral density exponent \(\beta = 0\).

Parameters

  • t (float) – the right hand endpoint of the time interval \([0,t]\) for the process

  • rng (numpy.random.Generator) – a custom random number generator

sample(n)

Generate a realization of colored noise.

Generate a colored noise realization with n increments.

Parameters

n (int) – the number of increments to generate.

property t

End time of the process.

times(n)

Generate times associated with n increments on [0, t].

Parameters

n (int) – the number of increments