Select all of the statements about the discrete-time Fourier series that are cor

Question

Select all of the statements about the discrete-time Fourier series that are correct.

1. The periodic signal x[n] can be real even if its associated Fourier series coefficients a_sub_k are complex valued.

2. The periodic signal x[n] can be written as a finite sum of complex exponentials.

3. The Fourier series coefficients are calculated using an integral.

4. A real and even periodic signal x[n] has only real and even Fourier series coefficients.

5. Convergence conditions as in the continuous-time case must be considered to determine the existence of the discrete-time Fourier series.

Explanation / Answer

(1) is correct , because    F{ Re[x(n)]} = [X(k)+X*(-k)]/2

(2) is correct , because ,   x(n) =k x(k)ej2kn/N

(3) is incorrect ,because    X(k) =[n x(n)e-j2kn/N]/N

(4) is incorrect , beause real and even periodic signal x[n] have only real ourier series coefficients.

(5) incorrect

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