1. When the frequency band is selected we can specify the sampling rate and the characteristics of the pre-filter, which is also called as __________ filter.

A. Analog filter

B. Anti-aliasing filter

C. Analog & Anti-aliasing filter

D. None of the mentioned

2. What are the main characteristics of an Anti-aliasing filter?

A. Ensures that the bandwidth of the signal to be sampled is limited to the frequency range

B. To limit the additive noise spectrum and other interference, which corrupts the signal

C. All of the mentioned

D. None of the mentioned

3. In general, a digital system designer has better control of tolerances in a digital signal processing system than an analog system designer who is designing an equivalent analog system.

A. True

B. False

4. The selection of the sampling rate Fs=1/T, where T is the sampling interval, not only determines the highest frequency (Fs/2) that is preserved in the analog signal but also serves as a scale factor that influences the design specifications for digital filters.

A. True

B. False

5. What is the configuration of system for digital processing of an analog signal?

A. Analog signal|| Pre-filter -> D/A Converter -> Digital Processor -> A/D Converter -> Post-filter

B. Analog signal|| Pre-filter -> A/D Converter -> Digital Processor -> D/A Converter -> Post-filter

C. Analog signal|| Post-filter -> D/A Converter -> Digital Processor -> A/D Converter -> Pre-filter

D. None of the mentioned

6. In DM, further the two integrators at encoding are replaced by one integrator placed before the comparator, and then such system is called?

A. System-delta modulation

B. sigma-delta modulation

C. Source-delta modulation

D. None of the mentioned

7. What is the system function of the integrator that is modeled by the discrete time system?

A. H(z)=\(\frac{z^{-1}}{1-z^{-1}}\)

B. H(z)=\(\frac{z^{-1}}{1+z^{-1}}\)

C. H(z)=\(\frac{z^{z^1}}{1-z^1}\)

D. H(z)=\(\frac{z^{z^1}}{1+z^1}\)

8. What is the z-transform of sequence {dq(n)} i.e., Dq(z)= ?

A. \(H_s (z)X(z)- H_n (z)E(z)\)

B. \(H_s (z)X(z)+ H_n (z)E(z)\)

C. \(H_s (n)X(z)+ H_n (n)E(z)\)

D. \(H_n (z)X(z)- H_s (z)E(z)\)

9. The performance of the SDM system is determined by the noise system function Hn(z), which has a magnitude of?

A. \(|H_n (z)|=2 |sin \frac{πF}{F_s}|\)

B. \(|H_n (z)|=4 |sin \frac{πF}{F_s}|\)

C. \(|H_n (z)|=3 |sin \frac{πF}{F_s}|\)

D. \(|H_n (z)|= |sin \frac{πF}{F_s}|\)

10. The in-band quantization noise variance is given as?

A. \(\sigma_n^2=\int_{-B}^B |H_n (F)|^3 S_e (F)dF\)

B. \(\sigma_n^2=\int_{-B}^B |H_n (F)|^2 S_e (F)dF\)

C. \(\sigma_n^2=\int_{-B}^B |H_n (F)|^1 S_e (F)dF\)

D. None

11. 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

12. 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

13. 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

14. 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

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

A. DB

B. db

C. dB

D. All of the mentioned

16. 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 \(log_2\frac{P_x}{P_n}\)

17. 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

18. 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

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

20. 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 \(20log_{10} \frac{R}{σ_x}\)

21. 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

22. 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

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

A. True

B. False

23. Is when compared to other design techniques?

A. True

B. False

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

25. 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. \((1+\frac{aT}{2})Y(z)+(1-\frac{aT}{2})y(n-1)=\frac{bT}{2} (x(n)+x(n+1))\)

26. 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. \((1+\frac{aT}{2})Y(z)-(1+\frac{aT}{2}) z^{-1} Y(z)=\frac{bT}{2} (1+z^{-1})X(z)\)

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

28. 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