Alias-Free Smoothed Wigner Distribution Function for Discrete-Time Samples
Abstract
An alias-free Wigner distribution function (WDF), for a time waveform s(t) limited to total frequency extent F, is available if the time sampling increment delta is less than 1/F. Furthermore, the WDF can be efficiently numerically evaluated via fast Fourier transform (FFT) procedures if the FFT size N is greater than 2T/delta, where T is the effective duration of s(t). 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 2/D, respectively, the new tighter requirements are delta < 1/CF + 2/D), and N > (2T/Delta) + 4/B(Delta).
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 09, 1990
- Accession Number
- ADA229987
Entities
People
- Albert H. Nuttall
Organizations
- Naval Underwater Systems Center