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

  1. Feb 25, 2010 #1
    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)?
     
  2. jcsd
  3. Feb 26, 2010 #2

    CompuChip

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    Do you mean you want to perform

    [tex] \int_a^b U(t, \chi / t) \, dt [/tex]

    numerically?
     
  4. Mar 2, 2010 #3
    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)?
     
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