31. The frequency shift can be achieved by multiplying the bandpass signal as given in the equation x(t) = \(u_c (t) cos2π F_c t-u_s (t) sin2π F_c t\) by the quadrature carriers cos[2πFct] and sin[2πFct] and lowpass filtering the products to eliminate the signal components of 2Fc.
A. True
B. False
32. 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)= \(u_c (nT)cos2πF_c nT-u_s (nT)sin 2πF_c nT\)?
A. \((-1)^m u_c (mT_1)-u_s\)
B. \(u_s (mT_1-\frac{T_1}{2})(-1)^{m+k+1}\)
C. \((-1)^m u_c (mT_1)- u_s (mT_1-\frac{T_1}{2})(-1)^{m+k+1}\)
D. None
33. Which low pass signal component occurs at the rate of B samples per second with even-numbered samples of x(t)?
A. uc-lowpass signal component
B. us-lowpass signal component
C. uc & us-lowpass signal component
D. none of the mentioned
34. Which low pass signal component occurs at the rate of B samples per second with odd-numbered samples of x(t)?
A. uc – lowpass signal component
B. us – lowpass signal component
C. uc & us – lowpass signal component
D. none of the mentioned
35. What is the reconstruction formula for the bandpass signal x(t) with samples taken at the rate of 2B samples per second?
A. \(\sum_{m=-\infty}^{\infty}x(mT)\frac{sin(π/2T) (t-mT)}{(π/2T)(t-mT)} cos2πF_c (t-mT)\)
B. \(\sum_{m=-\infty}^{\infty}x(mT)\frac{sin(π/2T) (t+mT)}{(π/2T)(t+mT)} cos2πF_c (t-mT)\)
C. \(\sum_{m=-\infty}^{\infty}x(mT)\frac{sin(π/2T) (t-mT)}{(π/2T)(t-mT)} cos2πF_c (t+mT)\)
D. \(\sum_{m=-\infty}^{\infty}x(mT)\frac{sin(π/2T) (t+mT)}{(π/2T)(t+mT)} cos2πF_c (t+mT)\)
36. What is the new center frequency for the increased bandwidth signal?
A. Fc‘= Fc+B/2+B’/2
B. Fc‘= Fc+B/2-B’/2
C. Fc‘= Fc-B/2-B’/2
D. None of the mentioned
37. According to the sampling theorem for low pass signals with T1=1/B, then what is the expression for uc(t) = ?
A. \(\sum_{m=-∞}^∞ u_c (mT_1)\frac{sin(\frac{π}{T_1}) (t-mT_1)}{(π/T_1)(t-mT_1)}\)
B. \(\sum_{m=-∞}^∞ u_s (mT_1-\frac{T_1}{2}) \frac{sin(\frac{π}{T_1}) (t-mT_1+T_1/2)}{(\frac{π}{T_1})(t-mT_1+\frac{T_1}{2})}\)
C. \(\sum_{m=-∞}^∞ u_c (mT_1)\frac{sin(\frac{π}{T_1}) (t+mT_1)}{(\frac{π}{T_1})(t+mT_1)}\)
D. \(\sum_{m=-∞}^∞ u_s (mT_1-\frac{T_1}{2}) \frac{sin(\frac{π}{T_1}) (t+mT_1+\frac{T_1}{2})}{(\frac{π}{T_1})(t+mT_1+\frac{T_1}{2})}\)
38. According to the sampling theorem for low pass signals with T1=1/B, then what is the expression for us(t) = ?
A. \(\sum_{m=-∞}^∞ u_c (mT_1) \frac{sin(\frac{π}{T_1}) (t-mT_1)}{(\frac{π}{T_1})(t-mT_1)}\)
B. \(\sum_{m=-∞}^∞ u_s (mT_1-\frac{T_1}{2}) \frac{sin(\frac{π}{T_1}) (t-mT_1+\frac{T_1}{2})}{(π/T_1)(t-mT_1+\frac{T_1}{2})}\)
C. \(\sum_{m=-∞}^∞ u_s (mT_1-\frac{T_1}{2}) \frac{sin(\frac{π}{T_1}) (t-mT_1-\frac{T_1}{2})}{(\frac{π}{T_1})(t-mT_1-\frac{T_1}{2})}\)
D. \(\sum_{m=-∞}^∞ u_c (mT_1) \frac{sin(\frac{π}{T_1}) (t+mT_1)}{(\frac{π}{T_1})(t+mT_1)}\)
39. What is the expression for low pass signal component uc(t) that can be expressed in terms of samples of the bandpass signal?
A. \(\sum_{n=-∞}^∞ (-1)^{n+r+1} x(2nT^{‘}-T^{‘}) \frac{sin(π/(2T^{‘})) (t-2nT^{‘}+T^{‘})}{(π/(2T^{‘}))(t-2nT^{‘}+T^{‘})}\)
B. \(\sum_{n=-∞}^∞ (-1)^n x(2nT^{‘}) \frac{sin(π/(2T^{‘})) (t-2nT^{‘})}{(π/(2T^{‘}))(t-2nT^{‘})}\)
C. All of the mentioned
D. None of the mentioned
40. What is the expression for low pass signal component us(t) that can be expressed in terms of samples of the bandpass signal?
A. \(\sum_{n=-∞}^∞ (-1)^{n+r+1} x(2nT^{‘}-T^{‘}) \frac{sin(π/(2T^{‘})) (t-2nT^{‘}+T^{‘})}{(π/(2T^{‘}))(t-2nT^{‘}+T^{‘})}\)
B. \(\sum_{n=-∞}^∞ (-1)^n x(2nT^{‘}) \frac{sin(π/(2T^{‘})) (t-2nT^{‘})}{(π/(2T^{‘}))(t-2nT^{‘})}\)
C. All of the mentioned
D. None of the mentioned