Hi, I need help with some basic fourier transform properties stuff - its fairly simple though I think I am doing something wrong.(adsbygoogle = window.adsbygoogle || []).push({});

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)e^{i*2*π*f*a}

so I have the function

cos(2πf_{0}x - π/4)

I know (from a previous question) that the fourier transform of cos(2πf_{0}x) is

½[δ(f+f_{0}) + δ(f-f_{0})]

where δ indicates the delta function.

so then if we factor above

cos(2πf_{0}x - π/4)

cos(2πf_{0}(x - 1/(8f_{0})))

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

{½[δ(f+f_{0}) + δ(f-f_{0})]} * exp(i*pi*f/(4f_{0})

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

Thanks

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# Fourier Properties (shifting)

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