Got Fourier Spectrum?

[ECE]

Im stuck, can anyone help me with this?

Calculate the fourier spectrum of a sinewave with a total total period of 1ms and a peak amplitude of 1000 mV

 

[Iron Woode]

Let me think about that.....

mmmm...nope.

 

[vshah]

post it in highly technical and you'll get an answer

 

[dighn]

this is from my lecture notes from last term, don't rmember this stuff too clearly off hand

there's an easy way to calculate the fouriur transform of a period signal from the fourier series coeeficients.

it's X(jw) = sum(k = -inf to inf, 2*pi*ak*delta(w-kb)) where b is the fundamental frequency of the period signal and ak is the fourier coefficient.
fourier series coefficnets of sine is relatively easy to get by expanding into exponentials and matching up coefficients with the foruier series form (1/2j for k = 1, -1/2j for k = -1, 0 for other k's)

just plug it in and you get the spectrum for sin(wt)

you can get w from the period and the amplitude is just a linear coefficient which is unaffected by the transofmration