1. 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

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

A. True

B. False

3. Is when compared to other design techniques?

A. True

B. False

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

5. 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. \((1+\frac{aT}{2})Y(z)+(1-\frac{aT}{2})y(n-1)=\frac{bT}{2} (x(n)+x(n+1))\)

6. 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. \((1+\frac{aT}{2})Y(z)-(1+\frac{aT}{2}) z^{-1} Y(z)=\frac{bT}{2} (1+z^{-1})X(z)\)

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

8. 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

9. 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

11. 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

11. The general linear constant coefficient difference equation characterizing an LTI discrete time system is?

A. y(n)=-\(\sum_{k=1}^N a_k y(n-k)+\sum_{k=0}^N b_k x(n-k)\)

B. y(n)=-\(\sum_{k=0}^N a_k y(n-k)+\sum_{k=0}^N b_k x(n-k) \)

C. y(n)=-\(\sum_{k=1}^N a_k y(n)+\sum_{k=0}^N b_k x(n) \)

D. None of the mentioned

12. Which of the following is the rational system function of an LTI system characterized by the difference equation

y(n)=-\(\sum_{k=1}^N a_k y(n-k)+\sum_{k=0}^N b_k x(n-k)\)?

A. \(\frac{\sum_{k=0}^N b_k x(n-k)}{1+\sum_{k=0}^N a_k y(n-k)}\)

B. \(\frac{1+\sum_{k=1}^N a_k y(n-k)}{\sum_{k=0}^N b_k x(n-k)}\)

C. \(\frac{\sum_{k=0}^N b_k x(n-k)}{1+\sum_{k=1}^N a_k y(n-k)}\)

D. \(\frac{1+\sum_{k=0}^N a_k y(n-k)}{\sum_{k=0}^N b_k x(n-k)}\)

13. We can view y(n)=-\(\sum_{k=1}^N a_k y(n-k)+\sum_{k=0}^N b_k x(n-k)\) as the computational procedure (an algorithm) for determining the output sequence y(n) of the system from the input sequence x(n).

A. True

B. False

14. Which of the following is used in the realization of a system?

A. Delay elements

B. Multipliers

C. Adders

D. All of the mentioned

15. Computational complexity refers to the number of ____________

A. Additions

B. Arithmetic operations

C. Multiplications

D. None of the mentioned

16. The number of times a fetch from memory is performed per output sample is one of the factors used in the implementation of the system.

A. True

B. False

17. Which of the following refers to the number of memory locations required to store the system parameters, past inputs, past outputs, and any intermediate computed values?

A. Computational complexity

B. Finite world length effect

C. Memory requirements

D. None of the mentioned

18. Finite word length effects refer to the quantization effects that are inherent in any digital implementation of the system, either in hardware or software.

A. True

B. False

19. Which of the following are called finite word length effects?

A. Parameters of the system must be represented with finite precision

B. Computations are truncated to fit in the limited precision constraints

C. Whether the computations are performed in fixed-point or floating-point arithmetic

D. All of the mentioned

20. The factors Computational complexity, memory requirements, and finite word length effects are the ONLY factors influencing our choice of the realization of the system.

A. True

B. False

21. In general, an FIR system is described by the difference equation

y(n)=\(\sum_{k=0}^{M-1}b_k x(n-k)\).

A. True

B. False

22. What is the general system function of an FIR system?

A. \(\sum_{k=0}^{M-1}b_k x(n-k)\)

B. \(\sum_{k=0}^M b_k z^{-k}\)

C. \(\sum_{k=0}^{M-1}b_k z^{-k}\)

D. None of the mentioned

23. Which of the following is a method for implementing an FIR system?

A. Direct form

B. Cascade form

C. Lattice structure

D. All of the mentioned

24. How many memory locations are used for storage of the output point of a sequence of length M in direct form realization?

A. M+1

B. M

C. M-1

D. None of the mentioned

25. The direct form realization is often called a transversal or tapped-delay-line filter.

A. True

B. False

26. What is the condition of M, if the structure according to the direct form is as follows?

A. M even

B. M odd

C. All values of M

D. Doesn’t depend on the value of M

27. By combining two pairs of poles to form a fourth-order filter section, by what factor we have reduced the number of multiplications?

A. 25%

B. 30%

C. 40%

D. 50%

28. The desired frequency response is specified at a set of equally spaced frequencies defined by the equation?

A. \(\frac{\pi}{2M}\)(k+α)

B. \(\frac{\pi}{M}\)(k+α)

C. \(\frac{2\pi}{M}\)(k+α)

D. None of the mentioned

29. The realization of the FIR filter by frequency sampling realization can be viewed as a cascade of how many filters?

A. Two

B. Three

C. Four

D. None of the mentioned

30. What is the system function of all-zero filter or comb filter?

A. \(\frac{1}{M}(1+z^{-M} e^{j2πα})\)

B. \(\frac{1}{M}(1+z^M e^{j2πα})\)

C. \(\frac{1}{M}(1-z^M e^{j2πα})\)

D. \(\frac{1}{M}(1-z^{-M} e^{j2πα})\)