Alias-Free Wigner Distribution Function and Complex Ambiguity Function for Discrete-Time Samples

Abstract : If an arbitrary complex continuous waveform s(t) with finite overall frequency extent F Hertz is sampled with time increment Delta . On the other hand, it is commonly believed that aliasing of the corresponding Wigner distribution function (WDF) can only be avoided by sampling twice as fast; i.e., Delta < 1/(2F) is thought to be required. Alternatively, interpolation of the time data has been suggested as a means of circumventing aliasing of the WDF; however, the computational burden has proven excessive if done by sinc function interpolation. It is demonstrated here that this conjecture is false, and that the usual sampling criterion, Delta < 1/F, suffices for exact reconstruction of the original continuous WDF, as well as the complex ambiguity function (CAF), at all time, frequency locations, without an excessive amount of computational effort. Keywords: Interspersed aliasing lobes; Temporal correlation; Spectral correlation; Ambiguity function; Aliasing elimination; Discrete time sampling; Wigner distribution; Bandlimited spectrum; Diamond gating function; Interspersed sampling.