Fourier Transform: Find Without Integration

[skan]

hi ,

the question is to find the Fourier transform of the following eqn without using integration

d(t)= [c(-1.5t)]exp(jwat)

where
c(t)= Ao + E(Sumation)An*cos(nwot) + Bn sin(nwot) [fourier series formula]

I knwo to find the FT of the above Fourier series. But why is exp(jwat)
the frequency shift and why shud we shift by wa.

Thanks,
skan

 

[NateTG]

Please don't cross/double post.

I'm assuming that:
$$j=\sqrt{-1}$$
since you're a phyicist.

Then if you apply the euler equation:
$$e^{j\theta}=\cos \theta + j \sin \theta$$

you should see how the exponent affects the frequency.

 

[skan]

Sorry for the double post.

1.Thanks but I take the FT of c(t) first and then I shift all the impulse functions by wa.
can someone please explain why as i don't understand why this is done this way.

2.Also I thought that the Integral of an impulse function is 1, but here its says that the integral of a impulse function is a unit step function.

thanks

 

[skan]

I mean I read in my notes that the integral of a impulse function is a unit step function