Analysis of time series signals of wave fields using state vectors

Abstract

AbstractThis paper proposes a method of analysis of time seriesignals of wave fields by state vectors with regard to complex variablez and discrete time variable. The scalar product of these state vectors, the condition of completeness and operators acting on states are defined and basic equations arqderived. The z‐transformation and the convolution theorem are discussed. The present method is applied to the signal analysis by digital filters wherein the signals in the spatial coordinate of wave fields are converted to the time series signals. Two digital filters are introduced to perform Fresnel transform to express the wave propagation in the Fresnel zone. In this analysis, the filter must have characteristics of propagator transform. Further, amethod of reconstructing images as filter outputs is discussed; the hologram signal is converted to the time s eries signals and input to the filter which performs the Fresnel transformation. The result of image reconstruction by this method is compared with the result obtained by the conventional numerical image reconstruction method.