Question 11 : A linear time invariant system is characterized by the system function H(z)=1/(1-0.5z^-1 )+2/(1-3z^-1 ).What is the h(n) if the system is stable?
1. (0.5)ⁿu(n)-2(3)ⁿu(n)
2. (0.5)ⁿu(-n-1)-2(3)ⁿu(-n-1)
3. (0.5)ⁿu(-n-1)-2(3)ⁿu(n)
4. (0.5)ⁿu(n)-2(3)ⁿu(-n-1)
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Question 12 : What are the values of z for which the value of X(z)=∞?
1. Poles
2. Zeros
3. Solutions
4. None of the mentioned
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Question 13 : The N^th root of unity W_N is given as:
1. e^j2πN
2. e-j2πN
3. e^-j2π/N
4. e^j2π/N
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Question 14 : What is the z-transform of the signal x(n)=[3(2ⁿ)-4(3ⁿ)]u(n)?
1. 3/(1-2z^-1)-4/(1-3z^-1)
2. 3/(1+2z^-1)-4/(1+3z^-1)
3. 3/(1-2z)-4/(1-3z)
4. None of the mentioned
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Question 15 : What is the ROC of the system function H(z) if the discrete time LTI system is BIBO stable?
1. Entire z-plane, except at z=0
2. Entire z-plane, except at z=∞
3. Contain unit circle
4. None of the mentioned
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Question 16 : 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(πn/4)u(n) and the system is initially at rest?
1. (0.5)ⁿu(n)
2. 0.5(6.3)ⁿu(n)
3. 6.3(0.5)ⁿ
4. 6.3(0.5)ⁿu(n)
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Question 17 : Which of the following justifies the linearity property of z-transform?[x(n)↔X(z)].
1. x(n)+y(n) ↔X(z)Y(z)
2. x(n)+y(n) ↔X(z)+Y(z)
3. x(n)y(n) ↔X(z)+Y(z)
4. x(n)y(n) ↔X(z)Y(z)
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Question 18 : What is the one sided z-transform of x(n)=δ(n-k)?
1. z^-k
2. z^k
3. 0
4. 1
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Question 19 : If X(z) has M finite zeros and N finite poles, then which of the following condition is true?
1. |N-M| poles at origin(if N < M)
2. |N+M| zeros at origin(if N < M)
3. |N+M| poles at origin(if N < M)
4. |N-M| zeros at origin(if N < M)
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Question 20 : Sampling rate conversion by the rational factor I/D is accomplished by what connection of interpolator and decimator?
1. Parallel
2. Cascade
3. Convolution
4. None of the mentioned
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