# Fourier Properties (shifting)

1. Oct 21, 2014

### thatguy14

Hi, I need help with some basic fourier transform properties stuff - its fairly simple though I think I am doing something wrong.

So we know from the shifting property
if h(x) has the fourier transform H(f)
then h(x-a) has the fourier transform H(f)ei*2*π*f*a

so I have the function

cos(2πf0x - π/4)

I know (from a previous question) that the fourier transform of cos(2πf0x) is

½[δ(f+f0) + δ(f-f0)]

where δ indicates the delta function.

so then if we factor above

cos(2πf0x - π/4)
cos(2πf0(x - 1/(8f0)))

so then shouldn't the answer be that the fourier transform is

{½[δ(f+f0) + δ(f-f0)]} * exp(i*pi*f/(4f0)

I don't see if I did anything wrong here - and further, can this be simplified more?

Thanks

2. Oct 26, 2014