| Abstract: | The objective of this paper is to propose an FFT technique symmetrical for time and frequency, in which the symmetrization is done by introducing generating functions. By the symmetrical treatment, it becomes possible to derive several complementary relations in the time and frequency domains. Based on the idea of the symmetrical FFT technique, the phase problem of seismic waves is discussed not only in the frequency domain but also in the time domain. Furthermore, the deconvolution technique to evaluate the minimum-phase-shift and all-pass functions of seismic waves, which is not discussed sufficiently in earthquake engineering, is developed in the two domains. Numerical examples to present these basic ideas are also illustrated in the symmetrical framework. |
