Generalized Spectrogram is the generalized application of spectrogram.
S P x , w 1 , w 2 ( t , f ) = G x , w 1 ( t , f ) G x , w 2 ∗ ( t , f ) {\displaystyle S{P_{x,{w_{1}},{w_{2}}}}(t,f)={G_{x,{w_{1}}}}(t,f)G_{_{x,{w_{2}}}}^{*}(t,f)} , where G x , w 1 ( t , f ) = ∫ − ∞ ∞ w 1 ( t − τ ) x ( τ ) e − j 2 π f τ d τ {\displaystyle {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 }} G x , w 2 ( t , f ) = ∫ − ∞ ∞ w 2 ( t − τ ) x ( τ ) e − j 2 π f τ d τ {\displaystyle {G_{x,{w_{2}}}}\left({t,f}\right)=\int _{-\infty }^{\infty }{{w_{2}}\left({t-\tau }\right)x\left(\tau \right)\,{e^{-j2\pi \,f\,\tau }}d\tau }} For w 1 ( t ) = w 2 ( t ) = w ( t ) {\displaystyle w_{1}(t)=w_{2}(t)=w(t)} , it reduces to the classical spectrogram: S P x , w ( t , f ) = G x , w ( t , f ) G x , w ∗ ( t , f ) = | G x , w ( t , f ) | 2 {\displaystyle S{P_{x,w}}(t,f)={G_{x,w}}(t,f)G_{_{x,w}}^{*}(t,f)=|{G_{x,w}}(t,f)|^{2}}
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, it reduces to the classical spectrogram:
