Hi there. I'm starting with the Fourier transforms, and I'm having some trouble with my first exercise on this topic.
The problem says: Given (H(x) is the Heaviside unit step function).
a) Consider the odd extension for f and find its Fourier integral representation.
b) Using the previous incise calculate the value for
Well, for a) I think I should get the fourier transfor for the sign function, I don't know if this is right, but anyway I've defined the function like this:
Then the Fourier integral representation:
But g(x) is odd, then:
And the thing is that the integral for the cosine diverges as I see it, but I'm probably doing something wrong.