periodogram
Sign in to saveIn signal processing, a periodogram is an estimate of the spectral density of a signal. The term was coined by Arthur Schuster in 1898. Today, the periodogram is a component of more sophisticated methods (see spectral estimation). It is the most common tool for examining the amplitude vs frequency characteristics of FIR filters and window functions. FFT spectrum analyzers are also implemented as a time-sequence of periodograms.
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Article
7 sectionsContents
- Definition
- Computation
- Applications
- See also
- Notes
- References
- Further reading
In signal processing, a periodogram is an estimate of the spectral density of a signal. The term was coined by Arthur Schuster in 1898. Today, the periodogram is a component of more sophisticated methods (see spectral estimation). It is the most common tool for examining the amplitude vs frequency characteristics of FIR filters and window functions. FFT spectrum analyzers are also implemented as a time-sequence of periodograms.
==Definition== There are at least two different definitions in use today. One of them involves time-averaging, and one does not. Time-averaging is also the purview of other articles (Bartlett's method and Welch's method). This article is not about time-averaging. The definition of interest here is that the power spectral density of a continuous function, , is the Fourier transform of its auto-correlation function (see Cross-correlation theorem, Spectral density, and Wiener–Khinchin theorem): \mathcal{F}\{x(t)\circledast x^*(-t)\} = X(f)\cdot X^*(f) = \left| X(f) \right|^2.