Determining Signal Spectra from Fourier Transform: 100 kHz Impulse Train

[electricalcoolness]

Hello there,
if I have a impulse train as f(t) with a frequency of 100 khz, and cos(w_0*t) = g(t) with frequency of 10 khz, how do I go about determining the signal spectra, (i.e. harmonics n = 1,2,3...)? I determined the Fourier transform, but I get stuck as to what to do with it.

Thanks.

 

[chroot]

Can you please post the problem exactly as it was given to you?

- Warren

 

[electricalcoolness]

Determine the theoretical spectrum by determining the Fourier transofrm for the output x(t), in the problem given below.

x(t) = f(t)(g(t)

f(t) = cos(w_0*t), Frequency = 10 KHZ
g(t) = 20% duty cycle rectangular wave, pulse height = 1, baseline = 0, frequency = 100 KHZ

From what I know right now, it looks like the Fourier transform will be a since function with center frequency 100 KHZ and bands at +- 10 KHZ.
And I came up with F(W) = (Ts)*sinc(w_0*Ts/2 - n*ws)
Ts = 1/100 KHZ
Ws = 2*pi*100 KHZ

of Which I believe I am on the right track, but I don't know for sure.

I also don't understand how to use the Fourier transform to determine the power in the signal at sample frequency, twice sample frequency, three times sample frequency...

one more thing, am I correct in that once I have the amplitude at a sample frequency the power is just A^2/2 ?

Thanks Guys. :)

 

[abdo375]

I've just finished a signals & systems course so I'm not an expert, but i do believe that when you get the Fourier transform of the signal you "see" it in the frequency domain and to get the power of the frequency domain you just need to calculate \sum \abs(G(f)^2) about the former part I really need more explanation if I can help you.

 

[doodle]

...
From what I know right now, it looks like the Fourier transform will be a since function with center frequency 100 KHZ and bands at +- 10 KHZ.
And I came up with F(W) = (Ts)*sinc(w_0*Ts/2 - n*ws)
Ts = 1/100 KHZ
Ws = 2*pi*100 KHZ

of Which I believe I am on the right track, but I don't know for sure.

I doubt it. Multiplication in the time domain is equivalent to convolution in the freequency domain. So in X(w), you should see the sinc functions duplicated at two locations, with centers at 10kHz and -10kHz, and the magnitude halved. Recall how cosine functions appear in the frequency spectrum.

As for the power spectrum, squaring the absolute of X(w) should yield the result.