Aliasing in the AF-GDTFD and the discrete spectrogram

It has previously been claimed that many of the discrete time-frequency representations (TFRs), including the alias free generalized time-frequency distributions (AF-GDTFD), contain aliasing components. This paper shows that the class of AF-GDTFD does indeed displace both cross term and auto term energy in ways not characteristic of continuous TFRs, but this energy displacement does not satisfy our traditional definition of aliasing. Since the discrete time spectrogram is a member of the class of AF-GDTFD, it will displace energy in ways not characteristic of the continuous spectrogram. This paper creates a procedure by which this energy displacement can be properly understood. Since a discrete time TFR should be periodic in frequency, it is suggested that the displaced energy be interpreted as cross terms across the periodic boundary and not as aliasing.