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==Properties==
* '''Relation with [[Wigner distribution function|Wigner Distribution]]'''
:<math>\mathcal{SP}_{w_1,w_2}(t,f)(x,w) = Wig(w_1', w_2')*Wig(t,f)(x, w),</math>
:where <math>w_1'(s):=w_1(-s), w_2'(s):=w_2(-s)</math>
* '''Time marginal condition'''
:The generalized spectrogram <math>\mathcal{SP}_{w_1,w_2}(t,f)(x,w)</math> satisfies the time marginal condition if and only if <math>w_1w_2' = \delta</math>.
* '''Frequency marginal condition'''
:The generalized spectrogram <math>\mathcal{SP}_{w_1,w_2}(t,f)(x,w)</math> satisfies the frequency marginal condition if and only if <math>w_1w_2' = \delta</math>.
* '''Conservation of energy'''
:The generalized spectrogram <math>\mathcal{SP}_{w_1,w_2}(t,f)(x,w)</math> satisfies the conservation of energy if and only if <math>(w_1,w_2) = 1</math>.
* '''Real analysis'''
:The generalized spectrogram <math>\mathcal{SP}_{w_1,w_2}(t,f)(x,w)</math> is real if and only if <math>w_1=C w_2</math> for some <math>C\in \R</math>.
==References==
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