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)?

X (F) = ( frac{1}{2} [X_l (F-F_c)+X_l^* (F-F_c)] )

X (F) = ( frac{1}{2} [X_l (F-F_c)+X_l^* (F+F_c)] )

X (F) = ( frac{1}{2} [X_l (F+F_c)+X_l^* (F-F_c)] )

X (F) = ( frac{1}{2} [X_l (F-F_c)+X_l^* (-F-F_c)] )

What is the Fourier transform of x(t)?

X (F) = ( frac{1}{2} [X_l (F-F_c)+X_l^* (F-F_c)] )

X (F) = ( frac{1}{2} [X_l (F-F_c)+X_l^* (F+F_c)] )

X (F) = ( frac{1}{2} [X_l (F+F_c)+X_l^* (F-F_c)] )

X (F) = ( frac{1}{2} [X_l (F-F_c)+X_l^* (-F-F_c)] )

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

( sum_{n=- }^ (-1)^n x(2nT^{ }) frac{sin u2061( /(2T^{ })) (t-2nT^{ })}{( /(2T^{ }))(t-2nT^{ })} )

( sum_{n=- }^ (-1)^{n+r+1} x(2nT^{ }-T^{ }) frac{sin u2061( /(2T^{ })) (t-2nT^{ }+T^{ })}{( /(2T^{ }))(t-2nT^{ }+T^{ })} )

( sum_{n=- }^ (-1)^n x(2nT^{ }) frac{sin u2061( /(2T^{ })) (t-2nT^{ })}{( /(2T^{ }))(t-2nT^{ })} )

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

( sum_{n=- }^ (-1)^{n+r+1} x(2nT^{ }-T^{ }) frac{sin u2061( /(2T^{ })) (t-2nT^{ }+T^{ })}{( /(2T^{ }))(t-2nT^{ }+T^{ })} )

( sum_{n=- }^ (-1)^n x(2nT^{ }) frac{sin u2061( /(2T^{ })) (t-2nT^{ })}{( /(2T^{ }))(t-2nT^{ })} )

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

( 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})} )

( sum_{m=- }^ u_c (mT_1) frac{sin u2061( frac{ }{T_1}) (t-mT_1)}{( frac{ }{T_1})(t-mT_1)} )

( 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})} )

( 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})} )

( sum_{m=- }^ u_c (mT_1) frac{sin u2061( frac{ }{T_1}) (t+mT_1)}{( frac{ }{T_1})(t+mT_1)} )

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

( 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})} )

( sum_{m=- }^ u_c (mT_1) frac{sin u2061( frac{ }{T_1}) (t-mT_1)}{( /T_1)(t-mT_1)} )

( 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})} )

( sum_{m=- }^ u_c (mT_1) frac{sin u2061( frac{ }{T_1}) (t+mT_1)}{( frac{ }{T_1})(t+mT_1)} )

( 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})} )

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

( sum_{m=- infty}^{ infty}x(mT) frac{sin u2061( /2T) (t+mT)}{( /2T)(t+mT)} cos u20612 F_c (t-mT) )

( sum_{m=- infty}^{ infty}x(mT) frac{sin u2061( /2T) (t-mT)}{( /2T)(t-mT)} cos u20612 F_c (t-mT) )

( sum_{m=- infty}^{ infty}x(mT) frac{sin u2061( /2T) (t+mT)}{( /2T)(t+mT)} cos u20612 F_c (t-mT) )

( sum_{m=- infty}^{ infty}x(mT) frac{sin u2061( /2T) (t-mT)}{( /2T)(t-mT)} cos u20612 F_c (t+mT) )

( sum_{m=- infty}^{ infty}x(mT) frac{sin u2061( /2T) (t+mT)}{( /2T)(t+mT)} cos u20612 F_c (t+mT) )

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

uc & us lowpass signal component

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 )?

(u_s (mT_1- frac{T_1}{2})(-1)^{m+k+1} )

((-1)^m u_c (mT_1)- u_s (mT_1- frac{T_1}{2})(-1)^{m+k+1} )

11 + Mcqs in Sampling of Band Pass Signals in Digital Signal Processing Page 1 McqOptions

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 x_l(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 u_s(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 u_c(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 u_s(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 u_c(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> & u<sub>s</sub> lowpass signal component
D.	none of the mentioned
Answer» C. u<sub>c</sub> & u<sub>s</sub> lowpass signal component

Discussion

10.	What is the final result obtained by substituting F_c=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 F_ct] and sin[2 F_ct] and lowpass filtering the products to eliminate the signal components of 2F_c.
A.	True
B.	False
Answer» B. False

Discussion

Explore topic-wise MCQs in Digital Signal Processing.

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)?

What is the Fourier transform of x(t)?

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

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

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

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

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

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

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

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 )?

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.

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 x_l(t)?

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

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

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

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

What is the final result obtained by substituting F_c=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 )?

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 F_ct] and sin[2 F_ct] and lowpass filtering the products to eliminate the signal components of 2F_c.