Coefficients of Fourier series and power of rectangular signal

Thread Starter

username_unknown

Joined Feb 9, 2017
13
I need help with the following problem:

Derive the expression for coefficients of Fourier series in exponential form for the sequence of rectangular pulses (with amplitude A, period T and duration θ) shown in this image:


Derive the expression for signal power depending on the coefficients of Fourier series.

Attempt:



I don't know how to evaluate the signal power depending on the coefficients of Fourier series.

Average power is given by:

Average power is not dependent on Fourier series coefficients. Is this a mistake in evaluation?
Is the signal power depending on the coefficients of Fourier series equal to the average power?

How to evaluate the signal power depending on the coefficients of Fourier series?
 

MrAl

Joined Jun 17, 2014
7,590
Hi,

Try starting with Parseval's Theorem.
Integral f^2(t) dt = (1/2pi)* integral |F(jw)|^2 dw
both from -inf to +inf.
2pi=2*pi.

Historically, Parseval's predated Fourier's by 17 years.
 

WBahn

Joined Mar 31, 2012
25,751
You can also take a more direct route and write s(t) in terms of the Fourier Series representation and then expand out the terms in s^2(t). In doing so, you will discover that all cross product terms are identically zero leaving you with an expression for power in a very compact form (which is basically Parseval's Theorem) in terms of the Fourier coefficients.
 
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