Spectral density

spectral density

(or spectrum density, power spectrum.) The Fourier transform of the autocovariance function (see autocorrelation) of a stationary process. The spectral density is a function of frequency; its units are the units of variance per unit frequency. The spectral density can be interpreted as a decomposition of the variance of the process: the variance attributable to fluctuations within a frequency band is the integral of the spectral density within that frequency band. The spectral density is often estimated from a time series by smoothing the sample version of it (sometimes called the periodogram). This can be calculated as the Fourier transform of the sample autocovariance function, or more commonly (and equivalently) as the squared modulus of the Fourier transform of the time series itself.
See spectral function, continuous spectrum, discrete spectrum

Term edited 15 June 2020.

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