Fourier transform of piecewise function with gate functions

[haydez98]

Confusion with Fourier Transform and Step Function...clarification needed please :)

I am required to find the Fourier Transform of (without integration):
s(t) = 1 for 0 < t < 4; -t/2 for 4 < t < 6.

I understand that for:
s(t) = t for 0 < t < 1; 1 for t > 1
that this is the same as

$$s(t) = \int{\prod1(t-\frac{1}{2})}dt<br />$$
(integral of the gate function)

but what happens if t is -ve? does that mean that the gate function would be II(-t-x)?

after that, i believe that i can figure out the FT of s(t)
thanks in advance!

 

[MeisterJ]

have you figured this one out yet? we are learning about step functions and Fourier transforms but i haven't clarified if they can be negative? and if so, how?