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- W13640516 abstract "This chapter focuses on finite Fourier series, which is a finite sum of sine waves with periods and phases chosen so that it coincides exactly with a finite number of data plotted against time. A Fourier series is an infinite sum of sine waves that converges to a continuous signal defined over a finite time interval. In fact, the signal can have a finite number of discontinuities at which the Fourier series converges to the average of the left- and right-hand limits. A plot of the contribution to the variance versus the frequency of the harmonic as a Fourier line spectrum is considered in the chapter. The Fourier transform allows for a continuum of frequencies which will be needed if an infinite length signal is aperiodic. The Fourier transform is obtained by imagining that the duration of the continuous signal tends to infinity. Finally, the discrete Fourier transform is defined for an infinite sequence. Spectral analysis is primarily concerned with the identification of the different frequency components of a given signal. The phase information cannot be recovered from a spectrum. Various forms of Parseval's theorem are crucial for this." @default.
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- W13640516 date "1995-01-01" @default.
- W13640516 modified "2023-09-23" @default.
- W13640516 title "Describing signals in terms of frequency" @default.
- W13640516 doi "https://doi.org/10.1016/b978-034063171-3/50006-3" @default.
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