How to interpret Sympy inverse_fourier_transform response

[ken72]

I'm just starting to use Sympy for fourier transforms and am having difficulty interpreting the result. For example, I know the inverse transform of sin(pi*f)/(pi*f) is the unit pulse but I don't see how the response from Sympy describes the unit pulse:

from sympy import *
t=Symbol('t',real=True)
f=Symbol('f',real=True)
x=sin(pi*f)/(pi*f)
X=inverse_fourier_transform(x, f, t)
print 'X=', X
#X= Piecewise((-t/Abs(t) + 1, 4*t**2 > 1), (1, True))

The way I read it is X=-t/Abs(t)+1 for 4*t**2>1, and 1 otherwise. The unit pulse is 0 for t<-1/2 and t>1/2. I don't see how -t/Abs(t) + 1, 4*t**2 > 1 says this. If t=-1 for example, -t/Abs(t)+1 evaluates to -(-1)/1 + 1 = 2.

Can someone explain?

[Larz60+]

This explains how to get unit pulse: http://www.bogotobogo.com/python/OpenCV_...FT_DFT.php

[ken72]

Thanks. What I'm looking for is help in interpreting the Sympy response to the inverse_fourier_transform command.

[Larz60+]

Here maybe? http://docs.sympy.org/latest/modules/int..._transform