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The definition of spectrogram is
:<math>S{P_{x,w}}(t,f) = {G_{x,w}}(t,f)G_{_{x,w}}^*(t,f)=|{G_{x,w}}(t,f)|^2</math>,
where <math>{G_{x,{w_1}}}</math> denotes the [[Gabor transform|Gabor Transform]] of <math>x(t)</math>.
Based on the spectrogram, the '''generalized spectrogram''' is defined as:
:<math>S{P_{x,{w_1},{w_2}}}(t,f) = {G_{x,{w_1}}}(t,f)G_{_{x,{w_2}}}^*(t,f)</math>,
where:
:<math>{G_{x,{w_1}}}\left( {t,f} \right) = \int_{ - \infty }^\infty {{w_1}\left( {t - \tau } \right)x\left( \tau \right)\,{e^{ - j2\pi \,f\,\tau }}d\tau }</math>
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