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#1




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 taxis 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. Thank you. Last edited by de1337ed; 05032012 at 05:24 AM. 
#2




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. You get: 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.
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"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. Thank you to all the people who worked on the All About Circuits ebook. It is one of the best electronics books out there. I'm a recent BSEE grad from the University of Pittsburgh Last edited by count_volta; 05042012 at 01:54 AM. 
#3




The first part about using the wellknown shifting theorem is logical. Your derivation of the Fourier transform of the unshifted step (Heaviside) function needs a little more careful thought. I suggest you Google "Fourier Transform of the Heaviside Function" to gain some further insights  particularly as to the origin of the delta function term.

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fourier, function, shifted, step, transform 
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