Fourier transform of cos(wt) and cos(t).

[thomas49th]

Is there a difference? My notes are inconsistent and very poor. Google search doesn't seem to be having much use.

Which one transforms into pi(dirac(w+w0) + dirac(w-w0))?

Thanks
Thomas

 

[vela]

Neither since ω₀ doesn't appear in either function.

 

[thomas49th]

Okay Fourier transform of cos(w0t) and cos(t).

What do they transform into? I presume cos(w0t) is pi(dirac(w+w0) + dirac(w-w0))?

but what about cos(t). I'm guessing somewhere like pi(dirac(w+t) + dirac(w-t)) but is there some scaling factor?

 

[Dick]

Use cos(t)=(e^(it)+e^(-it))/2. You know the Fourier transform of e^(it) is a delta function, right?