11. For what number of zeros, the approximation is poor?
A. 3
B. 4
C. 5
D. 6
Answer: A
We observe that when the number of zeros is minimum, that is when M=3, the resulting frequency response is a relatively poor approximation to the desired response.
12. Which of the following pairs of M and N will give a perfect match?
A. 3,6
B. 3,4
C. 3,5
D. 4,5
Answer: D
When M is increased from three to four, we obtain a perfect match with the desired Butterworth filter not only for N=4 but for N=5, and in fact, for larger values of N.
13. Which of the following filters will have an impulse response as shown in the below figure?
A. Butterworth filters
B. Type-I Chebyshev filter
C. Type-II Chebyshev filter
D. None of the mentioned
Answer: C
The diagram that is given in the question is the impulse response of the type-II Chebyshev filter.
14. 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
Answer: B
Let us assume that hd(n) is specified for n > 0, and the digital filter is an all-pole filter.
15. 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)
Answer: D
In this method, we consider the cascade connection of the desired filter Hd(z) with the reciprocal, all zero filter 1/H(z).
16. 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
Answer: A
We excite the cascade configuration by the unit sample sequence δ(n). Thus the input to the inverse system 1/H(z) is hd(n) and the output is y(n). Ideally, yd(n)= δ(n).
17. What should be the value of y(n) at n=0?
A. 0
B. -1
C. 1
D. None of the mentioned
Answer: C
The condition that yd(0)=y(0)=1 is satisfied by selecting b0=hd(0).
18. The error between the desired output and actual output is represented by y(n).
A. True
B. False
Answer: A
For n > 0, y(n) represents the error between the desired output yd(n)=0 and the actual output.
19. 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
Answer: B
The parameters {ak} are selected to minimize the sum of squares of the error sequence.
20. By integrating the error equation with respect to the parameters {ak}, we obtain a set of linear equations.
A. True
B. False
Answer: B
By differentiating the square of the error sequence with respect to the parameters {ak}, it is easily established that we obtain the set of linear equations.
21. 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
Answer: D
In a practical design problem, the desired impulse response hd(n) is specified for a finite set of points, say 0 < n d(n).
22. The least squares method can also be used in a pole-zero approximation for Hd(z).
A. True
B. False
Answer: A
We know that we can perform pole-zero approximation for Hd(z) by using the least-squares method.
23. 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
Answer: C
Nevertheless, we can use the desired response hd(n) for n < M to construct an estimate of hd(n).
24. 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
Answer: A
The parameters {bk} are selected to determine the zeros of the filter that can be obtained where h(n)=hd(n).
25. The foregoing approach for determining the poles and zeros of H(z) is sometimes called Prony’s method.
A. True
B. False
Answer: A
We find the coefficients {bk} by pade approximation and find the coefficients {ak} by the least-squares method. Thus the foregoing approach for determining the poles and zeros of H(z) is sometimes called Prony’s method.
