Alright, so I am using the Convolution property of Fourier Transforms to find a function $f(x)$. So the obvious equation: $h(x) = f(x) \ast g(x)$.
Definitions:
$$g(x)=Rect\left[\frac x w \right]$$
h(x) = al*exp(-((abs((x-b1)./c1).^d)))+a2
a2 = 1.205e+004 ;
al = 1.778e+005 ;
b1 = 94.88 ;
c1 = 224.3 ;
d = 4.077 ;
That is, $$h(x)=a_1 \exp\left[-\left(\frac{|x-b_1|}{c_1}\right)^d \right]+a_2$$ with the constants defined above.
So I want to find $f(x)$ by fourier transforming everything. The only prblem is that I can not find the fourier transform of h(x). I have tried to use fft()
in matlab, FourierTransform[h,x,$\omega$]
in mathematica. In matlab, when I apply fft to both $h(x)$ and the Rect[]
function, I do not end up with a reasonable result after ifft
(most likely due to the zeros of sinc). However, in Mathematica, I can not even get a result for the FT of $h(x)$. The computer just sits and does nothing. So I am really stuck. I do not have enough math background to try and find the FT by hand. So if anyone has any advice (or a really fast computer that will actually perform the FT). Thank you!