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Fourier series

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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:


For the case when k is equal to zero, the integral becomes


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?
 
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