Two-window Spectrograms and their Integrals

We analyze in this paper some basic properties of two-window spectrograms, introduced in a previous work. This is achieved by the analysis of their kernel, in view of their immersion in the Cohen class of time-frequency representations. Further we introduce weighted averages of two-window spectrograms depending on varying window functions. We show that these new integrated representations improve some features of both the classical Rihaczek representation and the two-window spectrogram which in turns can be viewed as limit cases of them.