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verd
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Alright. So... Conceptually I completely understand what I'm doing. I'm just a bit confused about how, mechanically, to solve this.
I basically have the following:
W(w)=(1/2)[p2(w+6)+p2(w-6)]
Where p2(w) is a pulse of width 2. Of course, w is omega, and the +/-6 is the shift. This is a modulated signal and it's in the frequency domain. Now this is my problem...
w(t) is put into a squaring function, which produces z(t).
In this problem, the frequency domain is infinitely easier to work with than the time domain. So I know I can use Parseval's theorem, the special case for squaring a function. My problem is that I am then presented with the followingI'm using:
\int_{-\infty}^{\infty}x^2(t)dt=\frac{1}{2\pi}\int_{-\infty}^{\infty}|X(\omega)|^2d\omega
Can I say that
<br /> Z(\omega)=\frac{1}{2\pi}\int_{-\infty}^{\infty} | \frac{1}{2} <br /> [ p_{2}(\omega + 4)+p_{2}(\omega - 4)] |^2 d \omega<br />?How do I deal with this integral? Do I just simply take the integral of the height of W(w) from -7 to -5 and then from 5 to 7 and just add them?
Am I supposed to end up with T/2, where T=the width of my pulse??Any suggestions would be greatly appreciated. Thanks
I basically have the following:
W(w)=(1/2)[p2(w+6)+p2(w-6)]
Where p2(w) is a pulse of width 2. Of course, w is omega, and the +/-6 is the shift. This is a modulated signal and it's in the frequency domain. Now this is my problem...
w(t) is put into a squaring function, which produces z(t).
In this problem, the frequency domain is infinitely easier to work with than the time domain. So I know I can use Parseval's theorem, the special case for squaring a function. My problem is that I am then presented with the followingI'm using:
\int_{-\infty}^{\infty}x^2(t)dt=\frac{1}{2\pi}\int_{-\infty}^{\infty}|X(\omega)|^2d\omega
Can I say that
<br /> Z(\omega)=\frac{1}{2\pi}\int_{-\infty}^{\infty} | \frac{1}{2} <br /> [ p_{2}(\omega + 4)+p_{2}(\omega - 4)] |^2 d \omega<br />?How do I deal with this integral? Do I just simply take the integral of the height of W(w) from -7 to -5 and then from 5 to 7 and just add them?
Am I supposed to end up with T/2, where T=the width of my pulse??Any suggestions would be greatly appreciated. Thanks
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