Thread: Fourier Transforms question

Hi Im new to fourier transforms and need to know how to put the following into seperate parts

f(t) = e^-2t U(t-3)

f(t) = e^-t U(t-6)

Originally Posted by hunterage2000

Hi Im new to fourier transforms and need to know how to put the following into seperate parts

f(t) = e^-2t U(t-3)

f(t) = e^-t U(t-6)

Do you know the definition of the function U(t - a)? Do you know the definition of a Fourier trasnform?

What have you tried? Where are you stuck?

yeah thats the step function. I know the fourier transform definition formula but completely struggle with the maths of it.

Will f(t) = e^-2t U(t-3) be f(t) = 3, t < 0 e^-2t, t > 0

Originally Posted by hunterage2000

Hi Im new to fourier transforms and need to know how to put the following into seperate parts

f(t) = e^-2t U(t-3)

f(t) = e^-t U(t-6)

What MrF said, and what does "put the following into seperate parts" mean, is that what the question actually said?

CB

I mean the seperate parts of the graph as in

f(t) = 3, t > 0
e^-2t, t < 0

I dont know how to take f(t) = e^-2t U(t-3) and put it in the above form.

Originally Posted by hunterage2000

I mean the seperate parts of the graph as in

f(t) = 3, t > 0
e^-2t, t < 0

I dont know how to take f(t) = e^-2t U(t-3) and put it in the above form.

You are expected to know that the Heaviside Step Function U(t - a) = 1 if t > a and zero if t < a. That is why I asked in my first post!

If you don't know the definition, then at this level you are expected to find a reference that explains it. I would be very very surprised if your textbook or class notes did not define it.

And if you know that U(t) = 1 for t > 0 and 0 for t < 0 then you are expected to understand the effect of a transformation such as U(t) --> U(t - a).