Let ak be the Fourier series of a periodic continuous-time signal xt then the Fourier series for the signal Re xt is
The Fourier series for the signal Re {x(t)} can be found by taking the real part of each term in the Fourier series of x(t). Therefore, the Fourier series for Re {x(t)} would be:
Re {ak * exp(jkω0t)} = ak * cos(kω0t)
where ω0 is the fundamental frequency of the signal and k is an integer.
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