Alias-Free Smoothed Wigner Distribution Function for Discrete-Time Samples
Technical progress rept.
NAVAL UNDERWATER SYSTEMS CENTER NEW LONDON CT
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An alias-free Wigner distribution function WDF, for a time waveform st limited to total frequency extent F, is available if the time sampling increment delta is less than 1F. Furthermore, the WDF can be efficiently numerically evaluated via fast Fourier transform FFT procedures if the FFT size N is greater than 2Tdelta, where T is the effective duration of st. However, in order to suppress the undesired inherent oscillating interference terms in the WDF, it is necessary to smooth the WDF, or equivalently, weight the complex ambiguity function. This smoothing operation cannot be accomplished without the penalty in terms of sampling increment delta and FFT size N. In particular, if the smearings in the time and frequency domains of the WDF are 2 B and 2D, respectively, the new tighter requirements are delta 1CF 2D, and N 2TDelta 4BDelta.
- Statistics and Probability