The Zak transform and decimated spectrograms

In this paper, the interrelation between the Zak transform and the Generalized Discrete Time-Frequency Distribution (GDTFD) is examined. Starting with the discrete Zak transform, its definition is broadened to include arbitrary windows creating the Windowed Zak (WZ) transform. The WZ is then combined with the spectrogram. It is demonstrated that the spectrogram based upon the WZ, called the Zak-Spectrogram, is a generalization of the standard spectrogram. Next, building upon the idea of the weighted spectrogram, the weighted Zak-Spectrogram is used to produce a new class of GDTFD, called the Decimated GDTFD (DGDTFD). The Decimated GDTFD is similar to the GDTFD except it trades bandwidth for computational speed