Causal FFT treatment applicable to singularity functions

The objective of this paper is to present a method of causal FFT treatment which is available to not only approximately time-limited and band-limited functions but also singularity functions appearing frequently in earthquake engineering problems such as time domain response analyses and seismic record processing. By means of the causal FFT treatment for a singularity function, it is possible to determine several causal functions. The properties of the obtained causal functions are discussed in detail. The 0 second and 0 Hz value problems of engineering importance concerning the determination of the discrete singularity values of non-time-limited or non-band-limited functions are presented. Finally, by presenting numerical examples, several problems existing in the FFT analyses of singularity functions and a method to solve the problems are explained in detail.