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:
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.