This set of Digital Signal Processing Multiple Choice Questions & Answers (MCQs) focuses on “Backward Difference Method”.

1. The equation for Heq(s) is

a) True

b) False

View Answer

Explanation: The analog filter in the time domain is governed by the following difference equation,

2. What is the first backward difference of y(n)?

a) [y(n)+y(n-1)]/T

b) [y(n)+y(n+1)]/T

c) [y(n)-y(n+1)]/T

d) [y(n)-y(n-1)]/T

View Answer

Explanation: A simple approximation to the first order derivative is given by the first backward difference. The first backward difference is defined by

[y(n)-y(n-1)]/T

3. Which of the following is the correct relation between ‘s’ and ‘z’?

a) z=1/(1+sT)

b) s=1/(1+zT)

c) z=1/(1-sT)

d) None of the mentioned

View Answer

Explanation: We know that s=(1-z

^{-1})/T=> z=1/(1-sT).

a) z=0

b) z=0.5

c) z=1

d) None of the mentioned

View Answer

Explanation: Letting s=σ+jΩ in the equation z=1/(1-sT) and by letting σ=0, we get

|z-0.5|=0.5

Thus the image of the jΩ axis of the s-domain is a circle with centre at z=0.5 in z-domain.

5. What is the radius of the circle represented by the image of jΩ axis of the s-domain?

a) 0.75

b) 0.25

c) 1

d) 0.5

View Answer

Explanation: Letting s=σ+jΩ in the equation z=1/(1-sT) and by letting σ=0, we get

|z-0.5|=0.5

Thus the image of the jΩ axis of the s-domain is a circle of radius 0.5 centered at z=0.5 in z-domain.

6. The frequency response H(ω) will be considerably distorted with respect to H(jΩ).

a) True

b) False

View Answer

Explanation: Since jΩ axis is not mapped to the circle |z|=1, we can expect that the frequency response H(ω) will be considerably distorted with respect to H(jΩ).

7. The left half of the s-plane is mapped to which of the following in the z-domain?

a) Outside the circle |z-0.5|=0.5

b) Outside the circle |z+0.5|=0.5

c) Inside the circle |z-0.5|=0.5

d) Inside the circle |z+0.5|=0.5

View Answer

Explanation: The left half of the s-plane is mapped inside the circle of |z-0.5|=0.5 in the z-plane, which completely lies in the right half z-plane.

a) True

b) False

View Answer

Explanation: An analog high pass filter cannot be mapped to a digital high pass filter because the poles of the digital filter cannot lie in the correct region, which is the left-half of the z-plane(z < 0) in this case.

9. Which of the following is the correct relation between ‘s’ and ‘z’?

a) s=(1-z^{-1})/T

b) s=1/(1+zT)

c) s=(1+z^{-1})/T

d) None of the mentioned

View Answer

Explanation: We know that z=1/(1-sT)=> s=(1-z

^{-1})/T.

10. What is the z-transform of the first backward difference equation of y(n)?

d) None of the mentioned

View Answer

Explanation: The first backward difference of y(n) is given by the equation

[y(n)-y(n-1)]/T

Thus the z-transform of the first backward difference of y(n) is given as

.

**Sanfoundry Global Education & Learning Series – Digital Signal Processing.**

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