A comparative study of alias-free time-frequency representations

The purpose of this paper is to evaluate several discrete Wigner distribution (DWD) formulations proposed in the literature that claim to be "alias-free" and demonstrate that most of them do indeed contain aliasing terms. Furthermore, we identify classes of signals which will always give aliasing errors for each of these DWD formulations and we state the necessary conditions for each of the "advertised" alias-free methods to produce truly alias-free time-frequency representations (TFRs).<>