I am trying to calculate the Fourier Transform of $h(x)=1/x$
So I was thinking:
Since the FT of $g(x)=sign(x)$ is $G(f)=1/(i\pi f)$ ,
then using property of duality gives that $G(x)=1/(i\pi x)$ transforms to $g(-f)=-sign(f)$
Next I used scaling property, and it turns out that -going this way- $h(x)=1/x$ transforms to $H(f)=-\pi sign(i\pi f)=-i\pi^2 sign(f)$, which is different from MATLAB output $-i\pi sign(f)$
I've set MATLAB to be consistent with this definition:
$$F\{f(x)\}=\int_{-\infty}^{\infty}{f(x)exp(-i2\pi fx)dx}$$
Here I am using f as frequency $f=\omega/(2\pi)$ , and the properties used are shown here..
Any idea of what's happening?
Thanks in advance.-