1. Which of the following is the right way of representing of the equation that contains only the positive frequencies in a given x(t) signal?

A. X+(F)=4V(F)X(F)

B. X+(F)=V(F)X(F)

C. X+(F)=2V(F)X(F)

D. X+(F)=8V(F)X(F)

2. What is the equivalent time –domain expression of X+(F)=2V(F)X(F)?

A. F(+1)[2V(F)]*F(+1)[X(F)]

B. F(-1)[4V(F)]*F(-1)[X(F)]

C. F(-1)[V(F)]*F(-1)[X(F)]

D. F(-1)[2V(F)]*F(-1)[X(F)]

3. In time-domain expression, \(x_+ (t)=F^{-1} [2V(F)]*F^{-1} [X(F)]\). The signal x+(t) is known as

A. Systematic signal

B. Analytic signal

C. Pre-envelope of x(t)

D. Both Analytic signal & Pre-envelope of x(t)

4. In equation \(x_+ (t)=F^{-1} [2V(F)]*F^{-1} [X(F)]\), if \(F^{-1} [2V(F)]=δ(t)+j/πt\) and \(F^{-1} [X(F)]\) = x(t). Then the value of ẋ(t) is?

A. \(\frac{1}{π} \int_{-\infty}^\infty \frac{x(t)}{t+τ} dτ\)

B. \(\frac{1}{π} \int_{-\infty}^\infty \frac{x(t)}{t-τ} dτ\)

C. \(\frac{1}{π} \int_{-\infty}^\infty \frac{2x(t)}{t-τ} dτ\)

D. \(\frac{1}{π} \int_{-\infty}^\infty \frac{4x(t)}{t-τ} dτ\)

5. If the signal ẋ(t) can be viewed as the output of the filter with impulse response h(t) = 1/πt, -∞ < t < ∞ when excited by the input signal x(t) then such a filter is called as __________

A. Analytic transformer

B. Hilbert transformer

C. Both Analytic & Hilbert transformer

D. None of the mentioned

6. What is the frequency response of a Hilbert transform H(F)=?

A. \(\begin{cases}&-j (F>0) \\ & 0 (F=0)\\ & j (F<0)\end{cases}\)

B. \(\left\{\begin{matrix}-j & (F<0)\\0 & (F=0) \\j & (F>0)\end{matrix}\right. \)

C. \(\left\{\begin{matrix}-j & (F>0)\\0 &(F=0) \\j & (F<0)\end{matrix}\right. \)

D. \(\left\{\begin{matrix}j&(F>0)\\0 & (F=0)\\j & (F<0)\end{matrix}\right. \)

7. What is the equivalent lowpass representation obtained by performing a frequency translation of X+(F) to Xl(F)= ?

A. X+(F+FC.

B. X+(F-FC.

C. X+(F*FC.

D. X+(Fc-F)

8. What is the equivalent time domain relation of xl(t) i.e., lowpass signal?

A. \(x_l (t)=[x(t)+j ẋ(t)]e^{-j2πF_c t}\)

B. x(t)+j ẋ(t) = \(x_l (t) e^{j2πF_c t}\)

C. \(x_l (t)=[x(t)+j ẋ(t)]e^{-j2πF_c t}\) & x(t)+j ẋ(t) = \(x_l (t) e^{j2πF_c t}\)

D. None of the mentioned

9. If we substitute the equation \(x_l (t)= u_c (t)+j u_s (t)\) in equation x (t) + j ẋ (t) = xl(t) ej2πFct and equate real and imaginary parts on side, then what are the relations that we obtain?

A. x(t)=\(u_c (t) \,cos2π \,F_c \,t+u_s (t) \,sin2π \,F_c \,t\); ẋ(t)=\(u_s (t) \,cos2π \,F_c \,t-u_c \,(t) \,sin2π \,F_c \,t\)

B. x(t)=\(u_c (t) \,cos2π \,F_c \,t-u_s (t) \,sin2π \,F_c \,t\); ẋ(t)=\(u_s (t) \,cos2π \,F_c t+u_c (t) \,sin2π \,F_c \,t\)

C. x(t)=\(u_c (t) \,cos2π \,F_c t+u_s (t) \,sin2π \,F_c \,t\); ẋ(t)=\(u_s (t) \,cos2π \,F_c t+u_c (t) \,sin2π \,F_c \,t\)

D. x(t)=\(u_c (t) \,cos2π \,F_c \,t-u_s (t) \,sin2π \,F_c \,t\); ẋ(t)=\(u_s (t) \,cos2π \,F_c \,t-u_c (t) \,sin2π \,F_c \,t\)

10. In the relation, x(t) = \(u_c (t) cos2π \,F_c \,t-u_s (t) sin2π \,F_c \,t\) the low frequency components uc and us are called _____ of the bandpass signal x(t).

A. Quadratic components

B. Quadrature components

C. Triplet components

D. None of the mentioned

11. What is the other way of representing of bandpass signal x(t)?

A. x(t) = Re\([x_l (t) e^{j2πF_c t}]\)

B. x(t) = Re\([x_l (t) e^{jπF_c t}]\)

C. x(t) = Re\([x_l (t) e^{j4πF_c t}]\)

D. x(t) = Re\([x_l (t) e^{j0πF_c t}]\)

12. In the equation x(t) = Re\([x_l (t) e^{j2πF_c t}]\), What is the lowpass signal xl (t) is usually called the ___ of the real signal x(t).

A. Mediature envelope

B. Complex envelope

C. Equivalent envelope

D. All of the mentioned

13. If a possible representation of a band pass signal is obtained by expressing xl (t) as \(x_l (t)=a(t)e^{jθ(t})\) then what are the equations of a(t) and θ(t)?

A. a(t) = \(\sqrt{u_c^2 (t)+u_s^2 (t)}\) and θ(t)=\(tan^{-1}\frac{u_s (t)}{u_c (t)}\)

B. a(t) = \(\sqrt{u_c^2 (t)-u_s^2 (t)}\) and θ(t)=\(tan^{-1}\frac{u_s (t)}{u_c (t)}\)

C. a(t) = \(\sqrt{u_c^2 (t)+u_s^2 (t)}\) and θ(t)=\(tan^{-1}\frac{u_c (t)}{u_s (t)}\)

D. a(t) = \(\sqrt{u_s^2 (t)-u_c^2 (t)}\) and θ(t)=\(tan^{-1}\frac{u_s (t)}{u_c (t)}\)

14. What is the possible representation of x(t) if xl(t)=a(t)e(jθ(t))?

A. x(t) = a(t) cos[2πFct – θ(t)]

B. x(t) = a(t) cos[2πFct + θ(t)]

C. x(t) = a(t) sin[2πFct + θ(t)]

D. x(t) = a(t) sin[2πFct – θ(t)]

15. In the equation x(t) = a(t)cos[2πFct+θ(t)], Which of the following relations between a(t) and x(t), θ(t) and x(t) are true?

A. a(t), θ(t) are called the Phases of x(t)

B. a(t) is the Phase of x(t), θ(t) is called the Envelope of x(t)

C. a(t) is the Envelope of x(t), θ(t) is called the Phase of x(t)

D. none of the mentioned

16. The basic task of the A/D converter is to convert a discrete set of digital code words into a continuous range of input amplitudes.

A. True

B. False

17. What is the type of quantizer, if a Zero is assigned a quantization level?

A. Midrise type

B. Mid tread type

C. Mistreat type

D. None of the mentioned

18. What is the type of quantizer, if a Zero is assigned a decision level?

A. Midrise type

B. Mid tread type

C. Mistreat type

D. None of the mentioned

19. What is the term used to describe the range of an A/D converter for bipolar signals?

A. Full scale

B. FSR

C. Full-scale region

D. FS

20. What is the term used to describe the range of an A/D converter for uni-polar signals?

A. Full scale

B. FSR

C. Full-scale region

D. FSS

21. What is the fixed range of the quantization error eq(n)?

A. \(\frac{\Delta}{6}\) < e<sub>q</sub>(n) ≤ \(\frac{\Delta}{6}\)

B. \(\frac{\Delta}{4}\) < e<sub>q</sub>(n) ≤ \(\frac{\Delta}{4}\)

C. \(\frac{\Delta}{2}\) < e<sub>q</sub>(n) ≤ \(\frac{\Delta}{2}\)

D. \(\frac{\Delta}{16}\) < e<sub>q</sub>(n) ≤ \(\frac{\Delta}{16}\)