Unaliased discrete-time ambiguity function

Abstract

This paper presents a new analytical closed-form definition of the unaliased discrete-time ambiguity function. The new definition uses only the Nyquist rate and the same number of sampling points that would otherwise give an aliased spectrum with the existing definition. The discrete-time ambiguity function possesses properties and symmetry features that resemble those of the continuous-time counterpart. This paper also shows that the discrete-time ambiguity function possesses temporal and spectral correlation functions that are similar to and play the same role as those of the continuous-time counterparts. The new definition of the discrete-time ambiguity function is shown to be dual to that of the unaliased discrete time Wigner distribution given recently by the author [J. Acoust. Soc. Am. 93, 363–371 (1993)]. Specifically, it preserves all the continuous-time Fourier transform relations. Computer simulations are performed to validate the unaliasing property of the new definition.