Application of Gabors Elementary-Signal Theorem to Estimation of Nonstationary Human Spectral Response

This paper addresses the problem of forming sequential gain and phase estimates needed to permit direct study of time variations in human response. The conventional Fourier transform with "boxcar" data window is shown to be unsatisfactory. Gabor's theory of elementary signals is cited to show that Fourier transformation with Gaussian data weighting yields an optimum combination of spectral and time resolution. For this window the estimation procedure is constrained by the fundamental relationship σω . σt = ½ where σω, σt are the standard deviations of weights across the spectral and data windows, respectively. The Gabor (Gaussianweighted Fourier) transform is introduced. Some consequences of implementing this procedure are briefly discussed and empirical results are presented in verification.