Oct-04-2017, 04:35 AM
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:
Can someone explain?
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?