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I am reading a paper on numerical methods which requires a 2D function to be converted to a 1D function. Let U(t, omega) be the discrete Gabor transform of a sampled signal, where t is time (seconds) and omega is the angular frequency. U(t, omega) is stored in a 2D m-by-n matrix.

Now U(t, omega) must be converted to u(chi) = u(t * omega), where chi = (t * omega),by integration over constant chi.

How do I efficiently perform numerical integration over constant chi, given the 2D matrix U(t, omega)?

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# Constructing u(t * omega) from U(t, omega)

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