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BUILT-IN MATHEMATICA SYMBOL
PowerSpectralDensity
PowerSpectralDensity[data, 
]
estimates the power spectral density for data.
PowerSpectralDensity[data, , sspec]
estimates the power spectral density for data with smoothing specification sspec.
PowerSpectralDensity[tproc, ]
represents the power spectral density of a time series process tproc.
Details and Options
- PowerSpectralDensity is also known as the energy spectral density.
- PowerSpectralDensity[tproc, ] is defined for weakly stationary time series processes as
, where 
is defined as AbsoluteCorrelationFunction[proc, i]. - The following smoothing specifications sspec can be given:
-
c use c as a cutoff w use 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, , {c, w}] is computed as
, where 
is defined as AbsoluteCorrelationFunction[data, i]. - 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](Files/PowerSpectralDensity.en/10.png "TemplateBox[{{w, (, x, )}}, Abs]<=1")
, 
for ![TemplateBox[{x}, Abs]>1/2](Files/PowerSpectralDensity.en/12.png "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 
. - PowerSpectralDensity takes the FourierParameters option. Common settings for FourierParameters include:
-
default setting 
often used for time series 
general setting
New in 9
