Fourier Transform a shifted step function?
I sort of understand how to obtain the Fourier transform of a regular step function (0 when t<0, and A when t>=0), but how do you obtain the fourier transform if the function has been shifted right on the t-axis by T? I've been stuck on this for a while.
What I have as an equation is the following:
from -∞ to ∞.
I then turn this into
from T to ∞
I don't know how to proceed from here.
Last edited by de1337ed; 05-03-2012 at 06:24 AM.
First of all, this is useful for you.
So the final result will just be the F transform of the unit step multiplied by e^-jωT
Then as far as doing the problem, take the A out of the integral and take the integral of the exponential. I'm sure you know how to do that. Integral of exponential is an exponential. Remember to do the substitution rule aka u = -jwt and du = -jw.
-A/jω [ e^-jωt] evaluated at t = infinity and t = T
I end up with A/jw * e^-jwT
I'm not sure where the delta function comes from, but I didn't get one.
"The gift of mental power comes from God, if we concentrate our minds on that truth,we become in tune with this great power" Nikola Tesla
Science is nothing more than our feeble attempt to understand the mysteries of God. When we succeed, and claim to understand everything there is to know, we show our foolishness.
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I'm a recent BSEE grad from the University of Pittsburgh
Last edited by count_volta; 05-04-2012 at 02:54 AM.
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