Ah whoops, ignore this. I thought you wrote an ##a## for the upper limit, but it is an ##\infty##, as it should be.I don't think step 3 is correct. the original function is not zero for |x| > a. But it looks like you assume that so that you can make the integral over this range, instead of from minus infinity to infinity. At least, that looks like what you had in mind...
right. yes, you are using the same definition of the Fourier transform as they are. Which is good :)jennyjones said:bruce W i'm using the cosine transform, i made a picture of this formula for my textbook.
I think you meant to say the average of the values of the Fourier transform on either side of the point ##\omega=a##. If this is what you meant, then yes that's right. Was it a guess? You have good intuition if it was. Yeah, there is a specific theorem (which is pretty hard to find on the internet), as vela is hinting at. This theorem works for certain kinds of function, like the rectangular function.jennyjones said:Vela, do you know if i can than say |ω|= (∏/2+0)/2=∏/4 ?