Digital Signal Processing

Backward Difference Method

Question 1
Marks : +2 | -2
Pass Ratio : 33%
An analog high pass filter can be mapped to a digital high pass filter.
True
False
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.
Question 2
Marks : +2 | -2
Pass Ratio : 33%
The equation for Heq(s) is \\(\\frac{\\sum_{K=0}^M b_K s^K}{\\sum_{K=0}^N a_K s^K}\\).
True
False
Explanation:
The analog filter in the time domain is governed by the following difference equation,
Question 3
Marks : +2 | -2
Pass Ratio : 33%
Which of the following is the correct relation between ‘s’ and ‘z’?
s=(1-z-1)/T
s=1/(1+zT)
s=(1+z-1)/T
none of the mentioned
Explanation:
We know that z=1/(1-sT)=> s=(1-z-1)/T.
Question 4
Marks : +2 | -2
Pass Ratio : 33%
Which of the following is the correct relation between ‘s’ and ‘z’?
z=1/(1+sT)
s=1/(1+zT)
z=1/(1-sT)
none of the mentioned
Explanation:
We know that s=(1-z-1)/T=> z=1/(1-sT).
Question 5
Marks : +2 | -2
Pass Ratio : 33%
What is the first backward difference of y(n)?
[y(n)+y(n-1)]/T
[y(n)+y(n+1)]/T
[y(n)-y(n+1)]/T
[y(n)-y(n-1)]/T
Explanation:
A simple approximation to the first order derivative is given by the first backward difference. The first backward difference is defined by
Question 6
Marks : +2 | -2
Pass Ratio : 33%
What is the radius of the circle represented by the image of jΩ axis of the s-domain?
0.75
0.25
1
0.5
Explanation:
Letting s=σ+jΩ in the equation z=1/(1-sT) and by letting σ=0, we get
Question 7
Marks : +2 | -2
Pass Ratio : 33%
What is the center of the circle represented by the image of jΩ axis of the s-domain?
z=0
z=0.5
z=1
none of the mentioned
Explanation:
Letting s=σ+jΩ in the equation z=1/(1-sT) and by letting σ=0, we get
Question 8
Marks : +2 | -2
Pass Ratio : 33%
The left half of the s-plane is mapped to which of the following in the z-domain?
Outside the circle |z-0.5|=0.5
Outside the circle |z+0.5|=0.5
Inside the circle |z-0.5|=0.5
Inside the circle |z+0.5|=0.5
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.
Question 9
Marks : +2 | -2
Pass Ratio : 33%
The frequency response H(ω) will be considerably distorted with respect to H(jΩ).
True
False
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).
Question 10
Marks : +2 | -2
Pass Ratio : 33%
What is the z-transform of the first backward difference equation of y(n)?
\\(\\frac{1+z^{-1}}{T}\\) Y(z)
\\(\\frac{1-z^{-1}}{T}\\) Y(z)
\\(\\frac{1+z^1}{T}\\) Y(z)
None of the mentioned
Explanation:
The first backward difference of y(n) is given by the equation