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

[nkinar]

Hello---

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)?

 

[CompuChip]

Do you mean you want to perform

$$\int_a^b U(t, \chi / t) \, dt$$

numerically?

 

[nkinar]

Hello CompuChip--

Thank you very much for your response! Yes, I think that I would like to numerically perform the integration that you describe using U(t, omega) as a 2D m-by-n matrix. How would I proceed?

Why do you write (chi/t) as an argument to U(t, omega)?