Digital Signal Processing Multiple Choice Questions on “Least Squares Design Methods”.
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
Answer: B
Clarification: Let us assume that hd(n) is specified for n > 0, and the digital filter is an all-pole filter.
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)
Answer: D
Clarification: In this method, we consider the cascade connection of the desired filter Hd(z) with the reciprocal, all zero filter 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
Answer: A
Clarification: 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).
4. What should be the value of y(n) at n=0?
A. 0
B. -1
C. 1
D. None of the mentioned
Answer: C
Clarification: The condition that yd(0)=y(0)=1 is satisfied by selecting b0=hd(0).
5. The error between the desired output and actual output is represented by y(n).
A. True
B. False
Answer: A
Clarification: For n > 0, y(n) represents the error between the desired output yd(n)=0 and the actual output.
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
Answer: B
Clarification: The parameters {ak} are selected to minimize the sum of squares of the error sequence.
7. By integrating the error equation with respect to the parameters {ak}, we obtain set of linear equations.
A. True
B. False
Answer: B
Clarification: 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.
8. Which of the following operation is done on the sequence in least square design method?
A. Convolution
B. DFT
C. Circular convolution
D. Correlation
Answer: D
Clarification: In a practical design problem, the desired impulse response hd(n) is specified for a finite set of points, say 0 < n
9. The least squares method can also be used in a pole-zero approximation for Hd(z).
A. True
B. False
Answer: A
Clarification: We know that we can perform pole-zero approximation for Hd(z) by using the least squares method.
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
Answer: C
Clarification: Nevertheless, we can use the desired response hd(n) for n < M to construct an estimate of hd(n).
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
Answer: A
Clarification: The parameters {bk} are selected to determine the zeros of the filter that can be obtained where h(n)=hd(n).
12. The foregoing approach for determining the poles and zeros of H(z) is sometimes called Prony’s method.
A. True
B. False
Answer: A
Clarification: We find the coefficients {bk} by pade approximation and find the coefficients {ak} by least squares method. Thus the foregoing approach for determining the poles and zeros of H(z) is sometimes called as Prony’s method.