Digital Signal Processing

Analysis of LTI System in Z Domain

Question 1
Marks : +2 | -2
Pass Ratio : 11%
A linear time invariant system is said to be BIBO stable if and only if the ROC of the system function _____________
Includes unit circle
Excludes unit circle
Is an unit circle
None of the mentioned
Explanation:
For an LTI system, if the ROC of the system function includes the unit circle, then the systm is said to be BIBO stable.
Question 2
Marks : +2 | -2
Pass Ratio : 11%
If one or more poles are located near the unit circle, then the rate of decay of signal is _________
Slow
Constant
Rapid
None of the mentioned
Explanation:
If the magnitudes of the poles of the response of any system is almost equal to one, then the system decays very slowly or the transient will persist for a relatively long time.
Question 3
Marks : +2 | -2
Pass Ratio : 11%
What is the transient response of the system described by the difference equation y(n)=0.5y(n-1)+x(n) when the input signal is x(n)= 10cos(Ï€n/4)u(n) and the system is initially at rest?
(0.5)nu(n)
0.5(6.3)nu(n)
6.3(0.5)n
6.3(0.5)nu(n)
Explanation:
The system function for the system is
Question 4
Marks : +2 | -2
Pass Ratio : 44%
If all the poles have small magnitudes, then the rate of decay of signal is __________
Slow
Constant
Rapid
None of the mentioned
Explanation:
If the magnitudes of the poles of the response of any system is very small i.e., almost equal to zero, then the system decays very rapidly.
Question 5
Marks : +2 | -2
Pass Ratio : 11%
If pk, k=1,2,…N are the poles of the system and |pk| < 1 for all k, then the natural response of such a system is called as Transient response.
True
False
Explanation:
If |pk| < 1 for all k, then ynr(n) decays to 0 as n approaches infinity. In such a case we refer to the natural response of the system as the transient response.
Question 6
Marks : +2 | -2
Pass Ratio : 11%
What is the steady-state response of the system described by the difference equation y(n)=0.5y(n-1)+x(n) when the input signal is x(n)= 10cos(Ï€n/4)u(n) and the system is initially at rest?
13.56cos(Ï€n/4 -28.7o)
13.56cos(Ï€n/4 +28.7o)u(n)
13.56cos(Ï€n/4 -28.7o)u(n)
None of the mentioned
Explanation:
The system function for the system is
Question 7
Marks : +2 | -2
Pass Ratio : 22%
What is the unit step response of the system described by the difference equation?
[1.099+1.088(0.9)n.\\(cos(\\frac{\\pi}{3} n+5.2^o)\\)]u(n)
[1.099+1.088(0.9)n.\\(cos(\\frac{\\pi}{3} n-5.2^o)\\)]u(n)
[1.099+1.088(0.9)n.\\(cos(\\frac{\\pi}{3} n-5.2^o)\\)]
None of the mentioned
Explanation:
The system function is H(z)=\\(\\frac{1}{1-0.9z^{-1}+0.81z^{-2}}\\)
Question 8
Marks : +2 | -2
Pass Ratio : 11%
If all the poles of H(z) are inside the unit circle, then the system is said to be ____________
Only causal
Only BIBO stable
BIBO stable and causal
None of the mentioned
Explanation:
If all the poles of H(z) are inside an unit circle, then it follows the condition that |z|>r < 1, it means that the system is both causal and BIBO stable.
Question 9
Marks : +2 | -2
Pass Ratio : 11%
If all the poles of H(z) are outside the unit circle, then the system is said to be _____________
Only causal
Only BIBO stable
BIBO stable and causal
None of the mentioned
Explanation:
If all the poles of H(z) are outside an unit circle, it means that the system is neither causal nor BIBO stable.
Question 10
Marks : +2 | -2
Pass Ratio : 11%
If the ROC of the system function is the exterior of a circle of radius r < ∞, including the point z = ∞, then the system is said to be ___________
Stable
Causal
Anti causal
None of the mentioned
Explanation:
A linear time invariant system is said to be causal if and only if the ROC of the system function is the exterior of a circle of radius r < ∞, including the point z = ∞.