Explore topic-wise MCQs in Digital Signal Processing.

This section includes 15 Mcqs, each offering curated multiple-choice questions to sharpen your Digital Signal Processing knowledge and support exam preparation. Choose a topic below to get started.

1.

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
Answer» E.
Discussion
2.

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
Answer» D. none of the mentioned
Discussion
3.

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. \(\frac{1}{T_p} \int_{t_0}^{t_0+T_p} x(t)e^{j2πkF_0 t} dt\)
Answer» C. \(\frac{1}{T_p} \int_{t_0}^{t_0+T_p} x(t)e^{-j2πkF_0 t} dt\)
Discussion
4.

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
Answer» B. Phase spectrum
Discussion
5.

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
Answer» D. None of the mentioned
Discussion
6.

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. \(\sum_{k=-\infty}^{\infty}|c_k|^2\)
Answer» E.
Discussion
7.

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
Answer» B. False
Discussion
8.

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
Answer» C. \(c_0+2\sum_{k=1}^{\infty}|c_k|tan(2πkF_0 t+θ_k)\)
Discussion
9.

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

A. True
B. False
Answer» C.
Discussion
10.

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. \(\frac{1}{T_p} \int_{t_0}^{t_0+T_p} x(t)e^{j2πkF_0 t} dt\)
Answer» D. \(\frac{1}{T_p} \int_{t_0}^{t_0+T_p} x(t)e^{j2πkF_0 t} dt\)
Discussion
11.

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. \(\sum_{k=-\infty}^{\infty}c_{-k} e^{j2πkF_0 t}\)
Answer» B. \(\sum_{k=0}^{\infty}c_k e^{j2πkF_0 t}\)
Discussion
12.

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
Answer» B. Phase spectrum
Discussion
13.

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

A. c<sub>k</sub>=X(F<sub>0</sub>/k)
B. c<sub>k</sub>= 1/T<sub>P</sub> (X(F<sub>0</sub>/k))
C. c<sub>k</sub>= 1/T<sub>P</sub>(X(kF<sub>0</sub>))
D. None of the mentioned
Answer» D. None of the mentioned
Discussion
14.

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
Answer» D. None of the mentioned
Discussion
15.

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
Answer» E.
Discussion