This set of Digital Signal Processing Multiple Choice Questions & Answers (MCQs) focuses on “Structures for FIR Systems-1”.

1. In general, an FIR system is described by the difference equation y(n)=∑M−1k=0bkx(n−k).**a) True**

b) False

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

a) ∑M−1k=0bkx(n−k)

b) ∑Mk=0bkz−k**c) ∑M−1k=0bkz−k**

d) None of the mentioned

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

a) Direct form

b) Cascade form

c) Lattice structure**d) All of the mentioned**

4. 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

5. The direct form realization is often called a transversal or tapped-delay-line filter.**a) True**

b) False

6. 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 value of M

7. 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%**

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

a) π2M(k+α)

b) πM(k+α)**c) 2πM(k+α)**

d) None of the mentioned

9. The realization of FIR filter by frequency sampling realization can be viewed as cascade of how many filters?**a) Two**

b) Three

c) Four

d) None of the mentioned

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

a) 1M(1+z−Mej2πα)

b) 1M(1+zMej2πα)

c) 1M(1−zMej2πα)**d) 1M(1−z−Mej2πα)**

11. The zeros of the system function of comb filter are located at ______________

a) Inside unit circle**b) On unit circle**c) Outside unit circle

d) None of the mentioned

12. What is the system function of the second filter other than comb filter in the realization of FIR filter?

a) ∑Mk=0H(k+α)1−ej2π(k+α)Mz−1

b) ∑M−1k=0H(k+α)1+ej2π(k+α)Mz−1**c) ∑M−1k=0H(k+α)1−ej2π(k+α)Mz−1**

d) None of the mentioned

13. Where does the poles of the system function of the second filter locate?

a) e^{j2π(k+α)M}**b) e ^{j2π(k+α)/M}**

c) e

^{j2π(k-α)/M}

d) e

^{jπ(k+α)/M}

14. When the desired frequency response characteristic of the FIR filter is narrowband, most of the gain parameters {H(k+α)} are zero.**a) True**

b) False

15. Which of the following filters have a cascade realization as shown below?

a) IIR filter

b) Comb filter

c) High pass filter**d) FIR filter**

16. Which of the following is the application of lattice filter?

a) Digital speech processing

b) Adaptive filter

c) Electroencephalogram**d) All of the mentioned**

17. If we consider a sequence of FIR filer with system function H_{m}(z)=A_{m}(z), then what is the definition of the polynomial A_{m}(z)?

a) 1+∑mk=0αm(k)z−k**b) 1+∑mk=1αm(k)z−k**

c) 1+∑mk=1αm(k)zk

d) ∑mk=0αm(k)z−k

18. What is the unit sample response of the m^{th} filter?

a) h_{m}(0)=0 and h_{m}(k)=αm(k), k=1,2…m

b) h_{m}(k)=αm(k), k=0,1,2…m(αm(0)≠1)**c) h _{m}(0)=1 and h_{m}(k)=αm(k), k=1,2…m**

d) none of the mentioned

19. The FIR filter whose direct form structure is as shown below is a prediction error filter.**a) True**

b) False

20. What is the output of the single stage lattice filter if x(n) is the input?

a) x(n)+Kx(n+1)**b) x(n)+Kx(n-1)**

c) x(n)+Kx(n-1)+Kx(n+1)

d) Kx(n-1)

21. What is the output from the second stage lattice filter when two single stage lattice filers are cascaded with an input of x(n)?

a) K_{1}K_{2}x(n-1)+K_{2}x(n-2)

b) x(n)+K_{1}x(n-1)

c) x(n)+K_{1}K_{2}x(n-1)+K_{2}x(n-2)**d) x(n)+K _{1}(1+K_{2})x(n-1)+K_{2}x(n-2)**

22. What is the value of the coefficient α_{2}(1) in the case of FIR filter represented in direct form structure with m=2 in terms of K_{1} and K_{2}?

a) K_{1}(K_{2})

b) K_{1}(1-K_{2})**c) K _{1}(1+K_{2})**

d) None of the mentioned

23. The constants K_{1} and K_{2} of the lattice structure are called as reflection coefficients.**a) True**

b) False

24. If a three stage lattice filter with coefficients K_{1}=1/4, K_{2}=1/2 K_{3}=1/3, then what are the FIR filter coefficients for the direct form structure?

a) (1,8/24,5/8,1/3)

b) (1,5/8,13/24,1/3)

c) (1/4,13/24,5/8,1/3)**d) (1,13/24,5/8,1/3)**

25. What are the lattice coefficients corresponding to the FIR filter with system function H(z)= 1+(13/24)z^{-1}+(5/8)z^{-2}+(1/3)z^{-3}?

a) (1/2,1/4,1/3)

b) (1,1/2,1/3)**c) (1/4,1/2,1/3)**

d) None of the mentioned

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