Thread: fourier transform of sin(3w)*cos(w)/(w^2)

Can someone tell me how to calculate the inverse fourier transform of sin(3w)*cos(w)/(w^2)
I know that 2sin(aw)/w has an inverse fourier transform that is 1 when -a<t<a and zero otherwise and therefore the inverse fourier should be the convultion of two of these and some other thing...can you help me?

You mean the inverse of sinc is a rect (or box) function. The other function is cosinc which you'll need to find a way to invert.

Originally Posted by Mppl

Can someone tell me how to calculate the inverse fourier transform of sin(3w)*cos(w)/(w^2)
I know that 2sin(aw)/w has an inverse fourier transform that is 1 when -a<t<a and zero otherwise and therefore the inverse fourier should be the convultion of two of these and some other thing...can you help me?

This function has a non-integrable singularity at w=0, so I don't see how it can have a Fourier transform (direct or inverse).

When you say that it doesn't have a FT are you considering that it can be a transform of a discrete variable signal?

Where did the problem come from?

My signals and systems exam

OK, just wantd to be sure it wasn't a typo. I'm still thinking about how to do this and Opalg's comment. It should be pointed out that the Fourier transform of is which also seems to have a non-integrable singularity at .

Write



where . Now invert using the convolution theorem.