An overview of aliasing errors in discrete-time formulations of time-frequency representations

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Initial algorithms for computing the Wigner distribution and other time-frequency representations belonging to Cohen's fixed kernel class required that the input signal be 1) oversampled by at least a factor of two; 2) analytic; 3) explicitly or implicitly interpolated by at least a factor of two in order to avoid aliasing errors. Recently proposed algorithms claim that they provide alias-free results for signals sampled at or near the Nyquist rate without requiring oversampling. In this paper, we demonstrate that most of these claims are invalid. Since the Wigner distribution can be directly used to obtain any other time-frequency representation belonging to Cohen's fixed kernel class, we first evaluate several recently proposed discrete Wigner distribution formulations that claim to be "alias-free," and then, we proceed to identify classes of signals that will always give aliasing errors for each of the investigated discrete Wigner distribution formulations, even when the signal has been oversampled by at least a factor of two. Finally, we state the necessary conditions for each of the "advertised" alias-free methods to produce truly alias-free time-frequency representations. ©1997 IEEE.

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IEEE Transactions on Signal Processing





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