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

Explanation: Let us assume that h

_{d}(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) H_{d}(z), H(z)

b) 1/H_{d}(z), 1/H(z)

c) 1/H_{d}(z), H(z)

d) H_{d}(z), 1/H(z)

View Answer

Explanation: In this method, we consider the cascade connection of the desired filter H

_{d}(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

Explanation: We excite the cascade configuration by the unit sample sequence δ(n). Thus the input to the inverse system 1/H(z) is h

_{d}(n) and the output is y(n). Ideally, y

_{d}(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

View Answer

Explanation: The condition that y

_{d}(0)= y(0)=1 is satisfied by selecting b

_{0}=h

_{d}(0).

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

a) True

b) False

View Answer

Explanation: For n > 0, y(n) represents the error between the desired output y

_{d}(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) {b_{k}}

b) {a_{k}}

c) Both of the mentioned

d) None of the mentioned

View Answer

Explanation: The parameters {a

_{k}} are selected to minimize the sum of squares of the error sequence.

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

a) True

b) False

View Answer

Explanation: By differentiating the square of the error sequence with respect to the parameters {a

_{k}}, 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

View Answer

Explanation: In a practical design problem, the desired impulse response h

_{d}(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 h

_{d}(n).

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

a) True

b) False

View Answer

Explanation: We know that we can perform pole-zero approximation for H

_{d}(z) by using the least squares method.

10. In which of the following condition we can use the desired response h_{d}(n)?

a) n < M

b) n=M

c) n > M

d) none of the mentioned

View Answer

Explanation: Nevertheless, we can use the desired response h

_{d}(n) for n < M to construct an estimate of h

_{d}(n).

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

a) {b_{k}}

b) {a_{k}}

c) Both of the mentioned

d) None of the mentioned

View Answer

Explanation: The parameters {b

_{k}} are selected to determine the zeros of the filter that can be obtained where h(n)=h

_{d}(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

Explanation: We find the coefficients {b

_{k}} by pade approximation and find the coefficients {a

_{k}} 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.**

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