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This paper discusses the theoretical basis for representation of a speech signal by its short-time Fourier transform. The results of the theoretical studies were used to design a speech analysis-synthesis system which was simulated on a general-purpose laboratory digital computer system. The simulation uses the fast Fourier transform in the analysis stage and specially designed finite duration impulse response filters in the synthesis stage. The results of both the theoretical and computational studies lead to an understanding of the effect of several design parameters and elucidate the design tradeoffs necessary to achieve moderate information rate reductions.