# Dictionary:Fig F-18

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 *g*_{t} (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.