Dictionary:Fourier analysis

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(foor’ ēā,) The analytical representation of a waveform as a weighted sum of sinusoidal functions. Determining the amplitude and phase of cosine (or sine) waves of different frequencies into which a waveform can be decomposed. Fourier analysis can be thought of as a subset of the Fourier transform (q.v.). See Figure F-18. Opposite of Fourier synthesis. Named for Jean Baptiste Joseph Fourier (1768–1830), French mathematician.

FIG. F-18. (a) Fourier analysis involves finding the amplitude of frequency components for a waveform. The frequency-domain representation or spectrum G(f) of a discrete time function gt (waveform, seismic record trace, etc.) can be decomposed into a series of sinusoids by any of the following equivalent equations:
Where
If is a continuous waveform, the sum signs become integrals. (b) Fourier synthesis involves superimposing the components to reconstitute the waveform. For an antisymmetric sawtooth waveform, the first four components are:
. For a Fourier transform the limits are and and and constitute a Fourier-transform pair; see Figure F-19.


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