- #1
Steve Drake
- 53
- 1
I have this expression:
f(\tau) = 4 \pi \int \omega ^2 P_2[\cos (\omega \tau)] P(\omega) \, \mathrm{d}w \quad [1] where P_2 is a second order Legendre polynomial, and P(\omega) is some distribution function.
Now I am told that, given a data set of f(\tau), I can solve for P(\omega) 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 P(\omega) directly via Fourier transforming. How could I do this in say MATLAB or Mathematica?
Thanks
f(\tau) = 4 \pi \int \omega ^2 P_2[\cos (\omega \tau)] P(\omega) \, \mathrm{d}w \quad [1] where P_2 is a second order Legendre polynomial, and P(\omega) is some distribution function.
Now I am told that, given a data set of f(\tau), I can solve for P(\omega) 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 P(\omega) directly via Fourier transforming. How could I do this in say MATLAB or Mathematica?
Thanks