Power spectrum of periodic signal

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xxxyyyba

Joined Aug 7, 2012
289
This is not really homework question, but this category looks most appropriate to me :)
We know that periodic function can be writen in terms of complex Fourier coefficients:
\(f(t)=F_n_=_0+\sum_{n=-\infty,n\neq 0}^{n=\infty}F_ne^{jnw_0t}\), where \(F_n=\frac{1}{T}\int_{\tau}^{\tau+T}f(t)e^{-jnw_0t}dt\) and \(F_n_=_0\) is DC component. Power spectrum of signal is defined as \(S_1_1(nw_0)=\left | F_n \right |^{2}\), where \(\left | F_n \right |\) is modulus of complex Fourier coefficient \(F_n\).
We can draw power spectrum as function of both negative and positive discrete frequencies nw0. My question is, if I want to draw it only for positive discrete frequencies, I should multiply \(\left | F_n \right |^{2}\) by 2, right? Should \(\left | F_n_=0 \right |^{2}\) be also multiplied by 2?
 
Last edited:

WBahn

Joined Mar 31, 2012
24,850
Why exclude n=0 from the sum? Why not just get rid of the first term and let it appear naturally as part of the sum?
 
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