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I am confused between "power" and "average power" of Fourier series. Let this be a simple Fourier series of a periodic function $f(t)$ :

$f(t) =\frac{a_0}{2}+\ a_n\cos(n\pi tL)+ \ b_n \sin(n\pi tL)$

Power = $(\frac{a_0}{2})^2$ + $\frac{a_n^2}{2}$ + $\frac{b_n^2}{2}$

My concept here is power of a constant function $c$ is $c^2$ and power of cosine/sine wave is $(amplitude)^2/2$.

But if I correlate Fourier Series with Circuit Analysis, then "average" power would mean "power of DC component" and here DC component is $\frac{a_0}{2}$ ; so

Average power = $(\frac{a_0}{2})^2$

Am I correct ?

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  • $\begingroup$ "Power" is being defined in two separate places (math, circuits). There is no reason to assume they will have identical definitions. $\endgroup$ Mar 17, 2021 at 17:22

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I have the answer now. Actually for a signal we always define "average power". And average power DOES NOT mean "power of DC component".

I confused this terribly with Circuit Analysis because there the average value of cosine and sine is zero. So I mixed that up and thought that average power of cosine/ sine would also be zero, but that is not the case.

Average power of cosine/ sine is always $\ (amplitude)^2/2$ .

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