1. If the input analog signal is within the range of the quantizer, the quantization error eq (n) is bounded in magnitude i.e., |eq (n)| < Δ/2 and the resulting error is called?

A. Granular noise

B. Overload noise

C. Particulate noise

D. Heavy noise

2. If the input analog signal falls outside the range of the quantizer (clipping), eq (n) becomes unbounded and results in _____________

A. Granular noise

B. Overload noise

C. Particulate noise

D. Heavy noise

3. In the mathematical model for the quantization error eq (n), to carry out the analysis, what are the assumptions made about the statistical properties of eq (n)?

A. The error eq (n) is uniformly distributed over the range — Δ/2 < eq (n) < Δ/2.

B. The error sequence is a stationary white noise sequence. In other words, the error eq (m) and the error eq (n) for m≠n are uncorrelated.

C. The error sequence {eq (n)} is uncorrelated with the signal sequence x(n).

D. All of the above

4. What is the abbreviation of SQNR?

A. Signal-to-Quantization Net Ratio

B. Signal-to-Quantization Noise Ratio

C. Signal-to-Quantization Noise Region

D. Signal-to-Quantization Net Region

5. What is the scale used for the measurement of SQNR?

A. DB

B. db

C. dB

D. All of the mentioned

6. What is the expression for SQNR which can be expressed in a logarithmic scale?

A. 10 \(log_{10}\frac{P_x}{P_n}\)

B. 10 \(log_{10}\frac{P_n}{P_x}\)

C. 10 \(log_2\frac{P_x}{P_n}\)

D. 2 \(log_2\frac{P_x}{P_n}\)

7. In the equation SQNR = 10 \(log_{10}\frac{P_x}{P_n}\). what are the terms Px and Pn are called ___ respectively?

A. Power of the Quantization noise and Signal power

B. Signal power and power of the quantization noise

C. None of the mentioned

D. All of the mentioned

8. In the equation SQNR = 10 (log_{10}frac{P_x}{P_n}), what are the expressions of Px and Pn?

A. \(P_x=\sigma^2=E[x^2 (n)] \,and\, P_n=\sigma_e^2=E[e_q^2 (n)]\)

B. \(P_x=\sigma^2=E[x^2 (n)] \,and\, P_n=\sigma_e^2=E[e_q^3 (n)]\)

C. \(P_x=\sigma^2=E[x^3 (n)] \,and\, P_n=\sigma_e^2=E[e_q^2 (n)]\)

D. None of the mentioned

9. If the quantization error is uniformly distributed in the range (-Δ/2, Δ/2), the mean value of the error is zero then the variance Pn is?

A. \(P_n=\sigma_e^2=\Delta^2/12\)

B. \(P_n=\sigma_e^2=\Delta^2/6\)

C. \(P_n=\sigma_e^2=\Delta^2/4\)

D. \(P_n=\sigma_e^2=\Delta^2/2\)

10. By combining \(\Delta=\frac{R}{2^{b+1}}\) with \(P_n=\sigma_e^2=\Delta^2/12\) and substituting the result into SQNR = 10 \(log_{10} \frac{P_x}{P_n}\), what is the final expression for SQNR = ?

A. 6.02b + 16.81 + \(20log_{10}\frac{R}{σ_x}\)

B. 6.02b + 16.81\(20log_{10} \frac{R}{σ_x}\)

C. 6.02b − 16.81\(20log_{10} \frac{R}{σ_x}\)

D. 6.02b − 16.81 \(20log_{10} \frac{R}{σ_x}\)

11. In the equation SQNR = 6.02b + 16.81 – (20log_{10} frac{R}{σ_x}), for R = 6σx the equation becomes?

A. SQNR = 6.02b-1.25 dB

B. SQNR = 6.87b-1.55 dB

C. SQNR = 6.02b+1.25 dB

D. SQNR = 6.87b+1.25 dB

12. In IIR Filter design by the Bilinear Transformation, the Bilinear Transformation is a mapping from

A. Z-plane to S-plane

B. S-plane to Z-plane

C. S-plane to J-plane

D. J-plane to Z-plane

13. In Bilinear Transformation, aliasing of frequency components is been avoided.

A. True

B. False

14. Is when compared to other design techniques?

A. True

B. False

15. The approximation of the integral in y(t) = \(\int_{t_0}^t y'(τ)dt+y(t_0)\) by the Trapezoidal formula at t = nT and t0=nT-T yields equation?

A. y(nT) = \(\frac{T}{2} [y^{‘} (nT)+y^{‘} (T-nT)]+y(nT-T)\)

B. y(nT) = \(\frac{T}{2} [y^{‘} (nT)+y^{‘} (nT-T)]+y(nT-T)\)

C. y(nT) = \(\frac{T}{2} [y^{‘} (nT)+y^{‘} (T-nT)]+y(T-nT)\)

D. y(nT) = \(\frac{T}{2} [y^{‘} (nT)+y^{‘} (nT-T)]+y(T-nT)\)

16. We use y{‘}(nT)=-ay(nT)+bx(nT) to substitute for the derivative in y(nT) = \(\frac{T}{2} [y^{‘} (nT)+y^{‘} (nT-T)]+y(nT-T)\) and thus obtain a difference equation for the equivalent discrete-time system. With y(n) = y(nT) and x(n) = x(nT), we obtain the result as of the following?

A. \((1+\frac{aT}{2})Y(z)-(1-\frac{aT}{2})y(n-1)=\frac{bT}{2} [x(n)+x(n-1)]\)

B. \((1+\frac{aT}{n})Y(z)-(1-\frac{aT}{n})y(n-1)=\frac{bT}{n} [x(n)+x(n-1)]\)

C. \((1+\frac{aT}{2})Y(z)+(1-\frac{aT}{2})y(n-1)=\frac{bT}{2} (x(n)-x(n-1))\)

D. \((1+\frac{aT}{2})Y(z)+(1-\frac{aT}{2})y(n-1)=\frac{bT}{2} (x(n)+x(n+1))\)

17. The z-transform of below difference equation is?

\((1+\frac{aT}{2})Y(z)-(1-\frac{aT}{2})y(n-1)=\frac{bT}{2} [x(n)+ x(n-1)]\)

A. \((1+\frac{aT}{2})Y(z)-(1-\frac{aT}{2}) z^{-1} Y(z)=\frac{bT}{2} (1+z^{-1})X(z)\)

B. \((1+\frac{aT}{n})Y(z)-(1-\frac{aT}{2}) z^{-1} Y(z)=\frac{bT}{n} (1+z^{-1})X(z)\)

C. \((1+\frac{aT}{2})Y(z)+(1-\frac{aT}{n}) z^{-1} Y(z)=\frac{bT}{2} (1+z^{-1})X(z)\)

D. \((1+\frac{aT}{2})Y(z)-(1+\frac{aT}{2}) z^{-1} Y(z)=\frac{bT}{2} (1+z^{-1})X(z)\)

18. What is the system function of the equivalent digital filter? H(z) = Y(z)/X(z) = ?

A. \(\frac{(\frac{bT}{2})(1+z^{-1})}{1+\frac{aT}{2}-(1-\frac{aT}{2}) z^{-1}}\)

B. \(\frac{(\frac{bT}{2})(1-z^{-1})}{1+\frac{aT}{2}-(1+\frac{aT}{2}) z^{-1}}\)

C. \(\frac{b}{\frac{2}{T}(\frac{1-z^{-1}}{1+z^{-1}}+A.}\)

D. \(\frac{(\frac{bT}{2})(1-z^{-1})}{1+\frac{aT}{2}-(1+\frac{aT}{2}) z^{-1}}\) & \(\frac{b}{\frac{2}{T}(\frac{1-z^{-1}}{1+z^{-1}}+A.}\)

18. In the Bilinear Transformation mapping, which of the following are correct?

A. All points in the LHP of s are mapped inside the unit circle in the z-plane

B. All points in the RHP of s are mapped outside the unit circle in the z-plane

C. All points in the LHP & RHP of s are mapped inside & outside the unit circle in the z-plane

D. None of the mentioned

19. In Nth order differential equation, the characteristics of bilinear transformation, let z=rejw,s=o+jΩ Then for s = \(\frac{2}{T}(\frac{1-z^{-1}}{1+z^{-1}})\), the values of Ω, ℴ are

A. ℴ = \(\frac{2}{T}(\frac{r^2-1}{1+r^2+2rcosω})\), Ω = \(\frac{2}{T}(\frac{2rsinω}{1+r^2+2rcosω})\)

B. Ω = \(\frac{2}{T}(\frac{r^2-1}{1+r^2+2rcosω})\), ℴ = \(\frac{2}{T}(\frac{2rsinω}{1+r^2+2rcosω})\)

C. Ω=0, ℴ=0

D. None

21. In equation ℴ = \(\frac{2}{T}(\frac{r^2-1}{1+r^2+2rcosω})\), if r > 1 then ℴ > 0 and then mapping from s-plane to z-plane occurs in which of the following order?

A. LHP in s-plane maps into the inside of the unit circle in the z-plane

B. RHP in s-plane maps into the outside of the unit circle in the z-plane

C. All of the mentioned

D. None of the mentioned