A class of quadratic time-frequency represent at ions based on the short-time Fourier transform

Motivated by problems in signal analysis, we define a class of timefrequency representations which is based on the short-tinie Fourier transform and depends on two fixed windows. We show that this class can be viewed as a link between the classical Rihaczek representation and the spectrograrn. Correspondingly we formulate for this class a suitable general form of the uncertainty principle which have, as limit case, the uncertainty principles for the Rihaczek representation and for the spectrogram. We finally consider the questions of marginal distributions. We compute them in terms of convolutions with the windows and prove simple conditions for which average and standard deviation of the distributions in our class coincide with that of their marginals.