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Forums
Mathematics
Calculus
Calculating 1D spectrum from 2D spectrum
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[QUOTE="fresh_42, post: 6266277, member: 572553"] For the sake of completeness ([URL]https://en.wikipedia.org/wiki/Gabor_transform[/URL]): [ATTACH type="full" alt="1574631547672.png"]253274[/ATTACH] In our case we have $$ U_x(\tau \, , \,\omega)=\displaystyle{\int_{-1.9143+\tau}^{1.9143+\tau}}x(t)e^{-\pi(t-\tau)^2}e^{-i\omega t}\,dt ) $$ and I'm a bit confused whether ##t## or ##\tau## is meant, i.e. if we are talking about a simple variable substitution. I assume that the exponent ##-\omega t## is abbreviated by ##\chi## and we have such a substitution of the integral variable. The real case applications of the Gabor transform lives with approximations. So maybe the ##\alpha## in the Wikipedia article can be used to simplify the other terms of the integrand. Or - what could be as well - ##U(\chi)## is a sloppy notation for ##U(\tau,\chi)##. [/QUOTE]
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Mathematics
Calculus
Calculating 1D spectrum from 2D spectrum
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