An interpretation of the spectrogram for discrete-time signals

The spectrogram for continous-time signals can be expressed as a convolution of two Wigner distributions in the time-frequency plane. Definitions exist for the discrete-time spectrogram and the discrete-time Wigner distribution, each with its own periodicity in the frequency domain. The authors demonstrate how the discrete-time spectrogram is related to a convolution of discrete-time Wigner distributions in spite of this noticeable incompatibility concerning periodicity. The result can be considered as the counterpart of the relation existing for continuous-time signals