1
GATE ECE 2014 Set 3
Numerical
+2
-0
Let $${H_1}(z) = {(1 - p{z^{ - 1}})^{ - 1}},{H_2}(z) = {(1 - q{z^{^{ - 1}}})^{ - 1}}$$ , H(z) =$${H_1}(z)$$ +r $${H_2}$$. The quantities p, q, r are real numbers. Consider , p=$${1 \over 2}$$, q=-$${1 \over 4}$$ $$\left| r \right|$$ <1. If the zero H(z) lies on the unit circle, the r = ____________________________.
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2
GATE ECE 2014 Set 3
Numerical
+2
-0
The z-transform of the sequence x$$\left[ n \right]$$ is given by x(z)= $${1 \over {{{(1 - 2{z^{ - 1}})}^2}}}$$ , with the region of convergence $$\left| z \right| > 2$$. Then, $$x\left[ 2 \right]$$ is ____________________.
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3
GATE ECE 2014 Set 2
MCQ (Single Correct Answer)
+2
-0.6
The input-output relationship of a causal stable LTI system is given as
𝑦[𝑛] = 𝛼 𝑦[𝑛 − 1] + $$\beta $$ x[n].
If the impulse response h[n] of this system satisfies the condition $$\sum\limits_{n = 0}^\infty h $$[n] = 2, the relationship between α and is $$\alpha $$ and $$\beta $$ is
A
𝛼 = 1 − $${\beta \over 2}$$
B
𝛼 = 1 + $${\beta \over 2}$$
C
𝛼 = 2𝛽
D
𝛼 = −2𝛽
4
GATE ECE 2008
MCQ (Single Correct Answer)
+2
-0.6
In the following network (Fig.1), the switch is closed at t = 0 and the sampling starts from t=0. The sampling frequency is 10 Hz. GATE ECE 2008 Signals and Systems - Discrete Time Signal Z Transform Question 14 English

The samples x (n) (n=0, 1, 2,...........) are given by

A
5(1-$${e^{ - 0.05n}}$$)
B
$$5{e^{ - 0.05n}}$$
C
$$5(1 - {e^{ - 5n}})$$
D
$$5{e^{ - 5n}}$$
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