Power of first three harmonics of periodic signal

[etf]

We know that periodic function can be written in terms of complex Fourier coefficients:
$$f(t)=Fn0+\sum_{n=-\infty,n\neq 0}^{n=\infty}F_ne^{jnw_0t}$$, where $$Fn=\frac{1}{T}\int_{\tau}^{\tau+T}f(t)e^{-jnw_0t}dt$$ and $$Fn0$$ is DC component. Power spectrum of signal is defined as $$S11(nw_0)=\left | F_n \right |^{2}$$, where $$\left | F_n \right |$$ is modulus of complex Fourier coefficient $$F_n$$.
In book, they gave us some periodic signal to write it in terms of complex Fourier coefficients and calculate power of first three harmonics. What is power of first three harmonics? Is it $$\left | Fn1 \right |^{2}+\left | Fn2 \right |^{2}+\left | Fn3 \right |^{2}$$?

 

[rude man]

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Power spectrum of signal is defined as $$S11(nw_0)=\left | F_n \right |^{2}$$, where $$\left | F_n \right |$$ is modulus of complex Fourier coefficient $$F_n$$.

In book, they gave us some periodic signal to write it in terms of complex Fourier coefficients and calculate power of first three harmonics. What is power of first three harmonics? Is it $$\left | Fn1 \right |^{2}+\left | Fn2 \right |^{2}+\left | Fn3 \right |^{2}$$?

Not right. Start with the trigonometric series coefficients for which you hopefully know the power expression, then equate those coefficients to the F_n.

Or, perform (1/T) ∫_T f²(t)dt given f(t) = Σ F_nexp(jnω₀)t,
T = 2π/ω₀.