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

$\int_{-∞}^∞|X(F)|^2 dt $

$\int_{-∞}^∞|X^* (F)|^2 dt $

$\int_{-∞}^∞ X(F).X^*(F) dt $

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

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

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

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

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

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

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

$\sum_{k=-\infty}^{\infty}|c_k|$

$\sum_{k=-\infty}^{\infty}|c_k|^2$

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

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

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

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

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

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

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

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

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

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

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

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

$\sum_{k=0}^{\infty}c_k e^{j2πkF_0 t}$

$\sum_{k=-\infty}^{\infty}c_k e^{j2πkF_0 t}$

$\sum_{k=0}^{\infty}c_k e^{j2πkF_0 t}$

$\sum_{k=-\infty}^{\infty}c_k e^{-j2πkF_0 t}$

$\sum_{k=-\infty}^{\infty}c_{-k} e^{j2πkF_0 t}$

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

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

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

x(t) is absolutely integrable in any period

15 + Mcqs in Frequency Analysis Continuous Time Signal in Digital Signal Processing Page 1 McqOptions

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 c_k?$
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 \|c_k \|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

Explore topic-wise MCQs in Digital Signal Processing.

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

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

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

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

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

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

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.

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

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

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

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

WHAT_IS_THE_SPECTRUM_THAT_IS_OBTAINED_WHEN_WE_PLOT_|CK|_AS_A_FUNCTION_OF_FREQUENCY??$

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

What is the spectrum that is obtained when we plot |c_k |² as a function of frequencies kF₀, k=0,¬¨¬®¬¨¬±1,¬¨¬®¬¨¬±2..?#

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

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.

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

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.

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

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

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

Explore topic-wise MCQs in Digital Signal Processing.

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

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

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

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

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

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

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.

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

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

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

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

WHAT_IS_THE_SPECTRUM_THAT_IS_OBTAINED_WHEN_WE_PLOT_|CK|_AS_A_FUNCTION_OF_FREQUENCY??$

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

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

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

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

What is the spectrum that is obtained when we plot |c_k |² as a function of frequencies kF₀, k=0,¬¨¬®¬¨¬±1,¬¨¬®¬¨¬±2..?#