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**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

[tex]s(t) = \int{\prod1(t-\frac{1}{2})}dt

[/tex]

(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!