MATLAB: How to find a fourier inverse transform using MATLAB Program

Question

Hello, I need help in writing a MATLAB program to find the inverse fourier tansform as it involves integration from the limits 0 to infinity !

Answer 1

If you have the symbolic toolbox use ifourier() and multiply your function by the Heaviside function to give you an integration for [0 \infty)

   syms t v
   ifourier(exp(-v)*heaviside(v),v)

Keep in mind the convention used here for the Fourier and inverse pair.

The Fourier transform is

 X(\omega) = \int_{-\infty}^{\infty} x(t) e^{-i \omega t} dt

and the inverse is

 x(t) = \dfrac{1}{2\pi} \int_{-\infty}^{\infty} X(\omega) e^{i\omega t} d\omega