Explore topic-wise MCQs in Digital Signal Processing.

This section includes 11 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.

What is the basic relationship between the spectrum o f the real band pass signal x(t) and the spectrum of the equivalent low pass signal xl(t)?

A. X (F) = ( frac{1}{2} [X_l (F-F_c)+X_l^* (F-F_c)] )
B. X (F) = ( frac{1}{2} [X_l (F-F_c)+X_l^* (F+F_c)] )
C. X (F) = ( frac{1}{2} [X_l (F+F_c)+X_l^* (F-F_c)] )
D. X (F) = ( frac{1}{2} [X_l (F-F_c)+X_l^* (-F-F_c)] )
Answer» E.
Discussion
2.

What is the Fourier transform of x(t)?

A. X (F) = ( frac{1}{2} [X_l (F-F_c)+X_l^* (F-F_c)] )
B. X (F) = ( frac{1}{2} [X_l (F-F_c)+X_l^* (F+F_c)] )
C. X (F) = ( frac{1}{2} [X_l (F+F_c)+X_l^* (F-F_c)] )
D. X (F) = ( frac{1}{2} [X_l (F-F_c)+X_l^* (-F-F_c)] )
Answer» E.
Discussion
3.

What is the expression for low pass signal component us(t) that can be expressed in terms of samples of the bandpass signal?

A. ( sum_{n=- }^ (-1)^{n+r+1} x(2nT^{ }-T^{ }) frac{sin u2061( /(2T^{ })) (t-2nT^{ }+T^{ })}{( /(2T^{ }))(t-2nT^{ }+T^{ })} )
B. ( sum_{n=- }^ (-1)^n x(2nT^{ }) frac{sin u2061( /(2T^{ })) (t-2nT^{ })}{( /(2T^{ }))(t-2nT^{ })} )
C. All of the mentioned
D. None of the mentioned
Answer» B. ( sum_{n=- }^ (-1)^n x(2nT^{ }) frac{sin u2061( /(2T^{ })) (t-2nT^{ })}{( /(2T^{ }))(t-2nT^{ })} )
Discussion
4.

What is the expression for low pass signal component uc(t) that can be expressed in terms of samples of the bandpass signal?

A. ( sum_{n=- }^ (-1)^{n+r+1} x(2nT^{ }-T^{ }) frac{sin u2061( /(2T^{ })) (t-2nT^{ }+T^{ })}{( /(2T^{ }))(t-2nT^{ }+T^{ })} )
B. ( sum_{n=- }^ (-1)^n x(2nT^{ }) frac{sin u2061( /(2T^{ })) (t-2nT^{ })}{( /(2T^{ }))(t-2nT^{ })} )
C. All of the mentioned
D. None of the mentioned
Answer» C. All of the mentioned
Discussion
5.

According to the sampling theorem for low pass signals with T1=1/B, then what is the expression for us(t) = ?

A. ( sum_{m=- }^ u_c (mT_1) frac{sin u2061( frac{ }{T_1}) (t-mT_1)}{( frac{ }{T_1})(t-mT_1)} )
B. ( sum_{m=- }^ u_s (mT_1- frac{T_1}{2}) frac{sin u2061( frac{ }{T_1}) (t-mT_1+ frac{T_1}{2})}{( /T_1)(t-mT_1+ frac{T_1}{2})} )
C. ( sum_{m=- }^ u_s (mT_1- frac{T_1}{2}) frac{sin u2061( frac{ }{T_1}) (t-mT_1- frac{T_1}{2})}{( frac{ }{T_1})(t-mT_1- frac{T_1}{2})} )
D. ( sum_{m=- }^ u_c (mT_1) frac{sin u2061( frac{ }{T_1}) (t+mT_1)}{( frac{ }{T_1})(t+mT_1)} )
Answer» C. ( sum_{m=- }^ u_s (mT_1- frac{T_1}{2}) frac{sin u2061( frac{ }{T_1}) (t-mT_1- frac{T_1}{2})}{( frac{ }{T_1})(t-mT_1- frac{T_1}{2})} )
Discussion
6.

According to the sampling theorem for low pass signals with T1=1/B, then what is the expression for uc(t) = ?

A. ( sum_{m=- }^ u_c (mT_1) frac{sin u2061( frac{ }{T_1}) (t-mT_1)}{( /T_1)(t-mT_1)} )
B. ( sum_{m=- }^ u_s (mT_1- frac{T_1}{2}) frac{sin u2061( frac{ }{T_1}) (t-mT_1+T_1/2)}{( frac{ }{T_1})(t-mT_1+ frac{T_1}{2})} )
C. ( sum_{m=- }^ u_c (mT_1) frac{sin u2061( frac{ }{T_1}) (t+mT_1)}{( frac{ }{T_1})(t+mT_1)} )
D. ( sum_{m=- }^ u_s (mT_1- frac{T_1}{2}) frac{sin u2061( frac{ }{T_1}) (t+mT_1+ frac{T_1}{2})}{( frac{ }{T_1})(t+mT_1+ frac{T_1}{2})} )
Answer» B. ( sum_{m=- }^ u_s (mT_1- frac{T_1}{2}) frac{sin u2061( frac{ }{T_1}) (t-mT_1+T_1/2)}{( frac{ }{T_1})(t-mT_1+ frac{T_1}{2})} )
Discussion
7.

What is the new centre frequency for the increased bandwidth signal?

A. F<sub>c</sub> = F<sub>c</sub>+B/2+B /2
B. F<sub>c</sub> = F<sub>c</sub>+B/2-B /2
C. F<sub>c</sub> = F<sub>c</sub>-B/2-B /2
D. None of the mentioned
Answer» C. F<sub>c</sub> = F<sub>c</sub>-B/2-B /2
Discussion
8.

What is the reconstruction formula for the bandpass signal x(t) with samples taken at the rate of 2B samples per second?

A. ( sum_{m=- infty}^{ infty}x(mT) frac{sin u2061( /2T) (t-mT)}{( /2T)(t-mT)} cos u20612 F_c (t-mT) )
B. ( sum_{m=- infty}^{ infty}x(mT) frac{sin u2061( /2T) (t+mT)}{( /2T)(t+mT)} cos u20612 F_c (t-mT) )
C. ( sum_{m=- infty}^{ infty}x(mT) frac{sin u2061( /2T) (t-mT)}{( /2T)(t-mT)} cos u20612 F_c (t+mT) )
D. ( sum_{m=- infty}^{ infty}x(mT) frac{sin u2061( /2T) (t+mT)}{( /2T)(t+mT)} cos u20612 F_c (t+mT) )
Answer» B. ( sum_{m=- infty}^{ infty}x(mT) frac{sin u2061( /2T) (t+mT)}{( /2T)(t+mT)} cos u20612 F_c (t-mT) )
Discussion
9.

Which low pass signal component occurs at the rate of B samples per second with odd numbered samples of x(t)?

A. u<sub>c</sub> lowpass signal component
B. u<sub>s</sub> lowpass signal component
C. u<sub>c</sub> &amp; u<sub>s</sub> lowpass signal component
D. none of the mentioned
Answer» C. u<sub>c</sub> &amp; u<sub>s</sub> lowpass signal component
Discussion
10.

What is the final result obtained by substituting Fc=kB-B/2, T= 1/2B and say n = 2m i.e., for even and n=2m-1 for odd in equation x(nT)= (u_c (nT)cos 2 F_c nT-u_s (nT)sin 2 F_c nT )?

A. ((-1)^m u_c (mT_1)-u_s )
B. (u_s (mT_1- frac{T_1}{2})(-1)^{m+k+1} )
C. None
D. ((-1)^m u_c (mT_1)- u_s (mT_1- frac{T_1}{2})(-1)^{m+k+1} )
Answer» E.
Discussion
11.

The frequency shift can be achieved by multiplying the band pass signal as given in equation x(t) = (u_c (t) cos 2 F_c t-u_s (t) sin 2 F_c t ) by the quadrature carriers cos[2 Fct] and sin[2 Fct] and lowpass filtering the products to eliminate the signal components of 2Fc.

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