1. 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

2. 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

3. 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

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 the 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. \(\frac{\pi}{2M}\)(k+α)

B. \(\frac{\pi}{M}\)(k+α)

C. \(\frac{2\pi}{M}\)(k+α)

D. None of the mentioned

9. 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

10. 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. \(\frac{1}{M}(1-z^{-M} e^{j2πα})\)

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

A. Inside the 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. \(\sum_{k=0}^M \frac{H(k+α)}{1-e^{\frac{j2π(k+α)}{M}} z^{-1}}\)

B. \(\sum_{k=0}^{M-1} \frac{H(k+α)}{1+e^{\frac{j2π(k+α)}{M}} z^{-1}}\)

C. \(\sum_{k=0}^{M-1} \frac{H(k+α)}{1-e^{\frac{j2π(k+α)}{M}} z^{-1}}\)

D. None of the mentioned

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

A. ej2π(k+α)M

B. ej2π(k+α)/M

C. ej2π(k-α)/M

D. ejπ(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 is the application of lattice filter?

A. Digital speech processing

B. Adaptive filter

C. Electroencephalogram

D. All of the mentioned

16. If we consider a sequence of FIR filers with system function Hm(z)=Am(z), then what is the definition of the polynomial Am(z)?

A. \(1+\sum_{k=0}^m α_m (k)z^{-k}\)

B. \(1+\sum_{k=1}^m α_m (k)z^{-k}\)

C. \(1+\sum_{k=1}^m α_m (k)z^k \)

D. \(\sum_{k=0}^m α_m (k)z^{-k}\)

17. What is the unit sample response of the mth filter?

A. hm(0)=0 and hm(k)=αm(k), k=1,2…m

B. hm(k)=αm(k), k=0,1,2…m(αm(0)≠1)

C. hm(0)=1 and hm(k)=αm(k), k=1,2…m

D. none of the mentioned

18. The FIR filter whose direct form structure is as shown below is a prediction error filter.

A. True

B. False

19. 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)

20. 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. K1K2x(n-1)+K2x(n-2)

B. x(n)+K1x(n-1)

C. x(n)+K1K2x(n-1)+K2x(n-2)

D. x(n)+K1(1+K2)x(n-1)+K2x(n-2)

21. What is the value of the coefficient α2(1) in the case of FIR filter represented in direct form structure with m=2 in terms of K1 and K2?

A. K1(K2)

B. K1(1-K2)

C. K1(1+K2)

D. None of the mentioned

22. The constants K1 and K2 of the lattice structure are called reflection coefficients.

A. True

B. False

23. If a three-stage lattice filter with coefficients K1=1/4, K2=1/2 K3=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)

24. 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