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

Answer: D

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

Answer: C

We know that s=(1-z-1)/T=> z=1/(1-sT).

4. What is the center of the circle represented by the image of jΩ axis of the s-domain?
A. z=0
B. z=0.5
C. z=1
D. none of the mentioned

Answer: B

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 a center at z=0.5 in the 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

Answer: D

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 the z-domain.

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

Answer: A

Since the 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

Answer: C

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.

8. An analog high pass filter can be mapped to a digital high pass filter.

A. True
B. False

Answer: B

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

Answer: A

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)?

A. \(\frac{1+z^{-1}}{T}\) Y(z)
B. \(\frac{1-z^{-1}}{T}\) Y(z)
C. \(\frac{1+z^1}{T}\) Y(z)
D. None of the mentioned

Answer: B

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
\(\frac{1-z^{-1}}{T}\) Y(z).