1. Which of the following filter we use in least-square design methods?

A. All zero

B. All pole

C. Pole-zero

D. Any of the mentioned

2. Which of the following are cascaded in this method?

A. Hd(z), H(z)

B. 1/Hd(z), 1/H(z)

C. 1/Hd(z), H(z)

D. Hd(z), 1/H(z)

3. If δ(n) is the input, then what is the ideal output of yd(n)?

A. δ(n)

B. 0

C. u(n)

D. None of the mentioned

4. What should be the value of y(n) at n=0?

A. 0

B. -1

C. 1

D. None of the mentioned

5. The error between the desired output and actual output is represented by y(n).

A. True

B. False

6. Which of the following parameters are selected to minimize the sum of squares of the error sequence?

A. {bk}

B. {ak}

C. {bk} & {ak}

D. None of the mentioned

7. By integrating the error equation with respect to the parameters {ak}, we obtain a set of linear equations.

A. True

B. False

8. Which of the following operation is done on the sequence in the least-square design method?

A. Convolution

B. DFT

C. Circular convolution

D. Correlation

9. The least squares method can also be used in a pole-zero approximation for Hd(z).

A. True

B. False

10. In which of the following condition we can use the desired response hd(n)?

A. n < M

B. n=M

C. n > M

D. none of the mentioned

11. Which of the following parameters are used to determine zeros of the filter?

A. {bk}

B. {ak}

C. {bk} & {ak}

D. None of the mentioned

12. The foregoing approach for determining the poles and zeros of H(z) is sometimes called Prony’s method.

A. True

B. False

13. Wiener filter is an FIR least-squares inverse filter.

A. True

B. False

14. If h(n) is the impulse response of an LTI system and h_{I}(n) is the impulse response of the inverse LTI system, then which of the following is true?

A. h(n).h_{I}(n)=1

B. h(n).h_{I}(n)=δ(n)

C. h(n)*h_{I}(n)=1

D. h(n)*h_{I}(n)=δ(n)

15. If H(z) is the system function of an LTI system and H_{I}(z) is the system function of the inverse LTI system, then which of the following is true?

A. H(z)*H_{I}(z)=1

B. H(z)*H_{I}(z)=δ(n)

C. H(z).H_{I}(z)=1

D. H(z).H_{I}(z)=δ(n)

16. It is not desirable to restrict the inverse filter to FIR.

A. True

B. False

17. Which of the following method is used to restrict the inverse filter to be FIR?

A. Truncating h_{I}(n)

B. Expanding h_{I}(n)

C. Truncating H_{I}(z)

D. None of the mentioned

18. What should be the length of the truncated filter?

A. M

B. M-1

C. M+1

D. Infinite

19. Which of the following criterion can be used to optimize the M+1 filter coefficients?

A. Pade approximation method

B. Least squares error criterion

C. Least squares error criterion & Pade approximation method

D. None of the mentioned

20. Which of the following filters have a block diagram as shown in the figure?

A. Pade wiener filter

B. Pade FIR filter

C. Least squares FIR filter

D. Least squares wiener filter

21. The autocorrelation of the sequence is required to minimize ε.

A. True

B. False

22. Which of the following are required to minimize the value of ε?

A. r_{hh}(l)

B. r_{dh}(l)

C. d(n)

D. all of the mentioned

23. FIR filter that satisfies \(\sum_{k=0}^M b_k r_{hh} (k-l)=r_{dh} (l)\), l=0,1,…M is known as wiener filter.

A. True

B. False

24. What should be the desired response for an optimum wiener filter to be an approximate inverse filter?

A. u(n)

B. δ(n)

C. u(-n)

D. none of the mentioned

25. If the set of linear equations from the equation \(\sum_{k=0}^M b_k r_{hh} (k-l)=r_{dh} (l)\), l=0,1,…M are expressed in matrix form, then what is the type of matrix obtained?

A. Symmetric matrix

B. Skew symmetric matrix

C. Toeplitz matrix

D. Triangular matrix

26. What is the number of computations proportional to, in the Levinson-Durbin algorithm?

A. M

B. M^{2}

C. M^{3}

D. M^{1/2}