Steve Drake
- 53
- 1
I have this expression:
[tex]f(\tau) = 4 \pi \int \omega ^2 P_2[\cos (\omega \tau)] P(\omega) \, \mathrm{d}w \quad [1][/tex] where [itex]P_2[/itex] is a second order Legendre polynomial, and [itex]P(\omega)[/itex] is some distribution function.
Now I am told that, given a data set of [itex]f(\tau)[/itex], I can solve for [itex]P(\omega)[/itex] by either assuming a model for it or Fourier transforming Eq. [1]. I can do this by assuming a distribution, eg Gaussian, then putting it in the integral, but I do not understand how I can obtain [itex]P(\omega)[/itex] directly via Fourier transforming. How could I do this in say MATLAB or Mathematica?
Thanks
[tex]f(\tau) = 4 \pi \int \omega ^2 P_2[\cos (\omega \tau)] P(\omega) \, \mathrm{d}w \quad [1][/tex] where [itex]P_2[/itex] is a second order Legendre polynomial, and [itex]P(\omega)[/itex] is some distribution function.
Now I am told that, given a data set of [itex]f(\tau)[/itex], I can solve for [itex]P(\omega)[/itex] by either assuming a model for it or Fourier transforming Eq. [1]. I can do this by assuming a distribution, eg Gaussian, then putting it in the integral, but I do not understand how I can obtain [itex]P(\omega)[/itex] directly via Fourier transforming. How could I do this in say MATLAB or Mathematica?
Thanks