Question

For Fourier series of a real signal , which of the following is correct?

• A. The real part of exponential Fourier series Coefficient is odd symmetric
• B. The imaginary part of exponential Fourier series coefficient is odd symmetric.
• C. The magnitude of exponential Fourier series Coeffient is even symmetric .
• D. The phase of exponential Fourier series coefficient is even symmetric .
  

Answer 1

Answer: (B), (C)

The magnitude of exponential Fourier series Coeffient is even symmetric .

(a, d)
The complex magnitude spectrum is always even symmetric.
The spectrum of real Fourier series is one sided.
The complex phase spectrum is odd symmetry.
If Real of x(t) is even then $b_n=0$
$\therefore$ Phase defined as $ta{n}^{-1}\left[\frac{b_n}{a_n}\right]=0$
Hence, no information in the phase spectrum.