PowerSpectralDensity

PowerSpectralDensity[data,ω]
estimates the power spectral density for data.

PowerSpectralDensity[data,ω,sspec]
estimates the power spectral density for data with smoothing specification sspec.

PowerSpectralDensity[tproc,ω]
represents the power spectral density of a time series process tproc.

Details and OptionsDetails and Options

  • PowerSpectralDensity is also known as the energy spectral density.
  • PowerSpectralDensity[tproc,ω] is defined for weakly stationary time series processes as , where denotes CovarianceFunction[proc,h].
  • The following smoothing specifications sspec can be given:
  • cuse c as a cutoff
    wuse a window function w
    {c,w}use both a cutoff and a window function
  • For a window function w and positive integer c, PowerSpectralDensity[data,ω,{c,w}] is computed as , where is defined as CovarianceFunction[data,h].
  • By default, the cutoff c is chosen to be , where is the length of data, and the window function is DirichletWindow.
  • A window function is an even function such that , TemplateBox[{{w, (, x, )}}, Abs]<=1, for TemplateBox[{x}, Abs]>1/2, including standard windows such as HammingWindow, ParzenWindow, etc.
  • A window function can be given as a list of values , where , and it will be applied symmetrically in the vector case.
  • PowerSpectralDensity takes the FourierParameters option. Common settings for FourierParameters include:
  • default setting
    often used for time series
    general setting

ExamplesExamplesopen allclose all

Basic Examples  (3)Basic Examples  (3)

Estimate the power spectral density for some data:

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Calculate the power spectral density for a univariate time series:

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The sample power spectral density for a random sample from autoregressive time series:

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Calculate power spectral density with cutoff:

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Introduced in 2012
(9.0)