Abstract
The objectives of this paper are to present FFT technique, which can evaluate Hilbert transforms, complex envelopes, and generating functions in hyperfunction theory, and to show ideas to separate seismic waves into several meaningful components and to synthesize seismic waves with definite characters, by means of the FFT technique. Several examples of synthesized seismic waves, such as random waves with the same Fourier spectrum and similar time envelope properties, random waves with the same time envelope and similar spectrum properties, and waves with mixed properties of two observed seismic waves, are also presented.
