1. The Fourier series representation of any signal x(t) is defined as ___________

A. \(\sum_{k=-\infty}^{\infty}c_k e^{j2πkF_0 t}\)

B. \(\sum_{k=0}^{\infty}c_k e^{j2πkF_0 t}\)

C. \(\sum_{k=-\infty}^{\infty}c_k e^{-j2πkF_0 t}\)

D. \(\sum_{k=-\infty}^{\infty}c_{-k} e^{j2πkF_0 t}\)

2. Which of the following is the equation for the Fourier series coefficient?

A. \(\frac{1}{T_p} \int_0^{t_0+T_p} x(t)e^{-j2πkF_0 t} dt\)

B. \(\frac{1}{T_p} \int_{t_0}^∞ x(t)e^{-j2πkF_0 t} dt\)

C. \(\frac{1}{T_p} \int_{t_0}^{t_0+T_p} x(t)e^{-j2πkF_0 t} dt\)

D. \(\frac{1}{T_p} \int_{t_0}^{t_0+T_p} x(t)e^{j2πkF_0 t} dt\)

3. Which of the following is a Dirichlet condition with respect to the signal x(t)?

A. x(t) has a finite number of discontinuities in any period

B. x(t) has finite number of maxima and minima during any period

C. x(t) is absolutely integrable in any period

D. all of the mentioned

4. The equation x(t)=\(\sum_{k=-\infty}^{\infty}c_k e^{j2πkF_0 t}\) is known as analysis equation.

A. True

B. False

5. Which of the following is the Fourier series representation of the signal x(t)?

A. \(c_0+2\sum_{k=1}^{\infty}|c_k|sin(2πkF_0 t+θ_k)\)

B. \(c_0+2\sum_{k=1}^{\infty}|c_k|cos(2πkF_0 t+θ_k)\)

C. \(c_0+2\sum_{k=1}^{\infty}|c_k|tan(2πkF_0 t+θ_k)\)

D. None of the mentioned

6. The equation x(t)=\(a_0+\sum_{k=1}^∞(a_k cos2πkF_0 t – b_k sin2πkF_0 t)\) is the representation of Fourier series.

A. True

B. False

7. The equation of average power of a periodic signal x(t) is given as ___________

A. \(\sum_{k=0}^{\infty}|c_k|^2\)

B. \(\sum_{k=-\infty}^{\infty}|c_k|\)

C. \(\sum_{k=-\infty}^0|c_k|^2\)

D. \(\sum_{k=-\infty}^{\infty}|c_k|^2\)

8. What is the spectrum that is obtained when we plot |ck |2 as a function of frequencies kF0, k=0,±1,±2..?

A. Average power spectrum

B. Energy spectrum

C. Power density spectrum

D. None of the mentioned

9. What is the spectrum that is obtained when we plot |ck| as a function of frequency?

A. Magnitude voltage spectrum

B. Phase spectrum

C. Power spectrum

D. None of the mentioned

10. What is the equation of the Fourier series coefficient ck of an non-periodic signal?

A. \(\frac{1}{T_p} \int_0^{t_0+T_p} x(t)e^{-j2πkF_0 t} dt\)

B. \(\frac{1}{T_p} \int_{-\infty}^∞ x(t)e^{-j2πkF_0 t} dt\)

C. \(\frac{1}{T_p} \int_{t_0}^{t_0+T_p} x(t)e^{-j2πkF_0 t} dt\)

D. \(\frac{1}{T_p} \int_{t_0}^{t_0+T_p} x(t)e^{j2πkF_0 t} dt\)

11. Which of the following relation is correct between Fourier transform X(F) and Fourier series coefficient ck?

A. ck=X(F0/k)

B. ck= 1/TP (X(F0/k))

C. ck= 1/TP(X(kF0))

D. none of the mentioned

12. According to Parseval’s Theorem for non-periodic signal, \(\int_{-∞}^∞|x(t)|^2 dt\).

A. \(\int_{-∞}^∞|X(F)|^2 dt \)

B. \(\int_{-∞}^∞|X^* (F)|^2 dt \)

C. \(\int_{-∞}^∞ X(F).X^*(F) dt \)

D. All of the mentioned

13. What is the Fourier series representation of a signal x(n) whose period is N?

A. \(\sum_{k=0}^{N+1}c_k e^{j2πkn/N}\)

B. \(\sum_{k=0}^{N-1}c_k e^{j2πkn/N}\)

C. \(\sum_{k=0}^Nc_k e^{j2πkn/N}\)

D. \(\sum_{k=0}^{N-1}c_k e^{-j2πkn/N}\)

14. What is the expression for Fourier series coefficient ck in terms of the discrete signal x(n)?

A. \(\frac{1}{N} \sum_{n=0}^{N-1}x(n)e^{j2πkn/N}\)

B. \(N\sum_{n=0}^{N-1}x(n)e^{-j2πkn/N}\)

C. \(\frac{1}{N} \sum_{n=0}^{N+1}x(n)e^{-j2πkn/N}\)

D. \(\frac{1}{N} \sum_{n=0}^{N-1}x(n)e^{-j2πkn/N}\)

15. Which of the following represents the phase associated with the frequency component of discrete-time Fourier series(DTFS)?

A. ej2πkn/N

B. e-j2πkn/N

C. ej2πknN

D. none of the mentioned

16. The Fourier series for the signal x(n)=cos√2πn exists.

A. True

B. False

17. What are the Fourier series coefficients for the signal x(n)=cosπn/3?

A. c1=c2=c3=c4=0,c1=c5=1/2

B. c0=c1=c2=c3=c4=c5=0

C. c0=c1=c2=c3=c4=c5=1/2

D. none of the mentioned

18. What is the Fourier series representation of a signal x(n) whose period is N?

A. \(\sum_{k=0}^{\infty}|c_k|^2\)

B. \(\sum_{k=-\infty}^{\infty}|c_k|\)

C. \(\sum_{k=-\infty}^0|c_k|^2\)

D. \(\sum_{k=-\infty}^{\infty}|c_k|^2\)

19. What is the average power of the discrete time periodic signal x(n) with period N?

A. \(\frac{1}{N} \sum_{n=0}^{N}|x(n)|\)

B. \(\frac{1}{N} \sum_{n=0}^{N-1}|x(n)|\)

C. \(\frac{1}{N} \sum_{n=0}^{N}|x(n)|^2\)

D. \(\frac{1}{N} \sum_{n=0}^{N-1}|x(n)|^2 \)

20. What is the equation for the average power of discrete-time periodic signal x(n) with period N in terms of Fourier series coefficient ck?

A. \(\sum_{k=0}^{N-1}|c_k|\)

B. \(\sum_{k=0}^{N-1}|c_k|^2\)

C. \(\sum_{k=0}^N|c_k|^2\)

D. \(\sum_{k=0}^N|c_k|\)