- #1

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The question in the book wants me to find the Fourier Transform of signal f(t) = e^-at; from 0 to T

I know in order to find FT I have to do the following:

T

step 1: F(w) = ∫ f(t) * e^-jwt dt

0

T

step 2: ∫ e^-(a+jw)t dt [combine like terms]

0

step 3: [ e^-(a+jw)0 ] - [ e^-(a+jw)T ] [integrate over 0 to T]

step 4: 1 - e^-(a+jw)T [solve]

The book says the answer is:

1-e^-(jw+a)T

----------------------------

jw+a

How did the book get the denominator section of jw+a? I cant get from step 4 to the book answer. What am I missing here?