Problems with Fourier Transform

[mngeow]

Hi , I'm having problems with this fourier transform question from school.

If the Fourier transform of v(t) is V (f), show that the Fourier transform of e^(j2ft) * v(t) is V (f − f₀).

I know that the fourier transform of e^(j2ft) is d(f-nf_o) , where d(f-nf_o) is a unit impulse centered at -f_o Hz. I also know that V(f) = ∫^∞_-∞ v(t)e^-(j2ft) dt. Where V(f) is the fourier transform of v(t) , and n = 1. Equating both of the equations together , I'd get the result d(f-nf_o) * V(f).

I'm kinda stuck at this point.

 

[Miralipoor]

Hi, multiplication in time domain is equivalent of convolution in frequency domain.so you need calculate each part in frequency domain and then convolve them.any way I think your result of primary question is wrong.
Regards