Digital Signal Processing Questions and Answers – Least Squares Design Methods

This set of Digital Signal Processing Multiple Choice Questions & Answers (MCQs) focuses 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
View Answer

Answer: b
Explanation: 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)
View Answer

Answer: d
Explanation: 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
View Answer

Answer: a
Explanation: 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).
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4. What should be the value of y(n) at n=0?
a) 0
b) -1
c) 1
d) None of the mentioned
View Answer

Answer: c
Explanation: 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
View Answer

Answer: a
Explanation: For n > 0, y(n) represents the error between the desired output yd(n)=0 and the actual output.
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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
View Answer

Answer: b
Explanation: 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
View Answer

Answer: b
Explanation: 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.
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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
View Answer

Answer: d
Explanation: In a practical design problem, the desired impulse response hd(n) is specified for a finite set of points, say 0 < n <L where L ≫ N. In such a case, the correlation sequence can be computed from the finite sequence hd(n).

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

Answer: a
Explanation: We know that we can perform pole-zero approximation for Hd(z) by using the least squares method.
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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
View Answer

Answer: c
Explanation: 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
View Answer

Answer: a
Explanation: 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
View Answer

Answer: a
Explanation: 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.

Sanfoundry Global Education & Learning Series – Digital Signal Processing.

To practice all areas of Digital Signal Processing, here is complete set of 1000+ Multiple Choice Questions and Answers.

If you find a mistake in question / option / answer, kindly take a screenshot and email to [email protected]

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Manish Bhojasia - Founder & CTO at Sanfoundry
Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He lives in Bangalore, and focuses on development of Linux Kernel, SAN Technologies, Advanced C, Data Structures & Alogrithms. Stay connected with him at LinkedIn.

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