Digital Signal Processing

LTI System as Frequency Selective Filters

Question 1
Marks : +2 | -2
Pass Ratio : 100%
Which filter has a magnitude frequency response as shown in the plot given below?
Low pass Filter
High pass Filter
Band pass Filter
Band stop Filter
Explanation:
In the magnitude response shown in the question, the system is stopping a particular band of signals. Hence the filter is called as Band stop filter.
Question 2
Marks : +2 | -2
Pass Ratio : 100%
If hlp(n) denotes the impulse response of a low pass filter with frequency response Hlp(ω), then what is the frequency response of the high pass filter in terms of Hlp(ω)?
Hlp(ω-π/2)
Hlp(ω+π/2)
Hlp(ω-π)
Hlp(ω+π)
Explanation:
The impulse response of a high pass filter is simply obtained from the impulse response of the low pass filter by changing the signs of the odd numbered samples in hlp(n). Thus
Question 3
Marks : +2 | -2
Pass Ratio : 100%
If the phase ϴ(ω) of the system is linear, then the group delay of the system?
Increases with frequency of signal
Constant
Decreases with frequency of signal
Independent of frequency of signal
Explanation:
We know that the group delay of the system with phase ϴ(ω) is defined as
Question 4
Marks : +2 | -2
Pass Ratio : 100%
An ideal filter should have unity gain in their stop band.
True
False
Explanation:
For an ideal filter, in the magnitude response plot at the stop band it should have a sudden fall which means an ideal filter should have a zero gain at stop band.
Question 5
Marks : +2 | -2
Pass Ratio : 100%
A two pole low pass filter has a system function H(z)=\\(\\frac{b_0}{(1-pz^{-1})^2}\\), What is the value of ‘b0‘ such that the frequency response H(ω) satisfies the condition |H(Ï€/4)|2=1/2 and H(0)=1?
0.36
0.38
0.32
0.46
Explanation:
Given
Question 6
Marks : +2 | -2
Pass Ratio : 100%
An ideal filter should have zero gain in their stop band.
True
False
Explanation:
For an ideal filter, in the magnitude response plot at the stop band it should have a sudden fall which means an ideal filter should have a zero gain at stop band.
Question 7
Marks : +2 | -2
Pass Ratio : 100%
What is the system function for a two pole band pass filter that has the centre of its pass band at ω=π/2, zero its frequency response characteristic at ω=0 and at ω=π, and its magnitude response is 1/√2 at ω=4π/9?
\\(0.15\\frac{1-z^{-2}}{1+0.7z^{-2}}\\)
\\(0.15\\frac{1+z^{-2}}{1-0.7z^{-2}}\\)
\\(0.15\\frac{1-z^{-2}}{1-0.7z^{-2}}\\)
\\(0.15\\frac{1+z^{-2}}{1+0.7z^{-2}}\\)
Explanation:
Clearly, the filter must have poles at P1,2=re±jπ/2 and zeros at z=1 and z=-1. Consequently the system function is
Question 8
Marks : +2 | -2
Pass Ratio : 100%
The ‘Envelope delay’ or ‘Group delay’ is the time delay that the signal component of frequency ω undergoes as it passes from the input to the output of the system.
True
False
Explanation:
The time delay taken to reach the output of the system from the input by a signal component is called as envelope delay or group delay.
Question 9
Marks : +2 | -2
Pass Ratio : 100%
If the low pass filter described by the difference equation y(n)=0.9y(n-1)+0.1x(n) is converted into a high pass filter, then what is the frequency response of the high pass filter?
0.1/(1+0.9ejω)
0.1/(1+0.9e-jω)
0.1/(1-0.9ejω)
None of the mentioned
Explanation:
The difference equation for the high pass filter is
Question 10
Marks : +2 | -2
Pass Ratio : 100%
A two pole low pass filter has a system function H(z)=\\(\\frac{b_0}{(1-pz^{-1})^2}\\), What is the value of ‘p’ such that the frequency response H(ω) satisfies the condition |H(Ï€/4)|2=1/2 and H(0)=1?
0.46
0.38
0.32
0.36
Explanation:
Given