GATE ECE

Discrete Time Signal Z Transform

Signals and Systems

(Past Years Questions)

Marks 1

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A discrete time all-pass system has two of its poles at 0.25$$\angle 0^\circ $$ and $$\angle 30^\circ $$. Which one of t...
GATE ECE 2018
A discrete-time signal$$x\left[ n \right]\, = \delta \left[ {n - 3} \right]\, + 2\delta \left[ {n - 5} \right]$$ has z-t...
GATE ECE 2016 Set 3
Consider the sequence $$x\left[ n \right]$$= $${a^n}u\left[ n \right] + {b^{\partial n}}u\left[ n \right]$$ , where u[n...
GATE ECE 2016 Set 1
Two casual discrete-time signals $$x\left[ n \right]$$ and $$y\left[ n \right]$$ =$$\sum\limits_{m = 0}^n x \left[ m \ri...
GATE ECE 2015 Set 2
The sequence x $$\left[ n \right]$$ = $${0.5^n}$$ u[n], where u$$\left[ n \right]$$ is the unit step sequence, is conv...
GATE ECE 2014 Set 4
For an all-pass system H(z)= $${{({z^{ - 1}} - b)} \over {(1 - a{z^{ - 1}})}}$$ where $$\left| {H({e^{ - j\omega }})} ...
GATE ECE 2014 Set 3
An FIR system is described by the system function $$$H(z) = 1 + {7 \over 2}{z^{ - 1}} + {3 \over 2}{z^{ - 2}}$$$
GATE ECE 2014 Set 2
Let x$$\left[ n \right]$$ = x$$\left[- n \right]$$ . Let X(z) be the z-transform of x$$\left[ n \right]$$. if 0.5 +j 0.2...
GATE ECE 2014 Set 2
If $$x\left[ n \right]$$= $${(1/3)^{\left| n \right|}} - {(1/2)^n}u\left[ n \right]$$, then the region of convergence (R...
GATE ECE 2012
Consider the z-transform X(z)=5$${z^2} + 4{z^{ - 1}} + 3;0 The inverse z - transform x$$\,\left[ n \right]$$ is ...
GATE ECE 2010
The ROC of Z-transform of the discrete time sequence x(n)= $${\left( {{1 \over 3}} \right)^{n}}u(n) - {\left( {{1 \over...
GATE ECE 2009
If the region of convergence of $${x_1}\left[ n \right]$$ + $${x_2}\left[ n \right]$$ is 1/3...
GATE ECE 2006
The region of convergence of z-transform of the sequence $${\left( {{5 \over 6}} \right)^n}u(n) - {\left( {{6 \over 5}}...
GATE ECE 2005
The z transform of a system is H(z) = $${z \over {z - 0.2}}$$ . If the ROC is $$\left| {z\,} \right|$$ ...
GATE ECE 2004
The region of convergence of the z- transform of a unit step function is
GATE ECE 2001
The z-transform F(z) of the function f(nT) = $${a^{nT}}$$ is
GATE ECE 1999
The z - transform of the time function $$\sum\limits_{k = 0}^\infty {\delta \left( {n - k} \right)} $$ is
GATE ECE 1998

Marks 2

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The ROC (region of convergence) of the z-transform of a discrete-time signal is represented by the shaded region in the ...
GATE ECE 2016 Set 3
A sequence x$$\left[ n \right]$$ is specified as $$\left[ {\matrix{ {x\left[ n \right]} \cr {x\left[ {n - 1} \ri...
GATE ECE 2016 Set 1
A realization of a stable discrete time system is shown in the figure. If the system is excited by a unit step sequence ...
GATE ECE 2015 Set 3
Suppose x $$\left[ n \right]$$ is an absolutely summable discrete-time signal. Its z-transform is a rational function wi...
GATE ECE 2015 Set 3
The pole-zero diagram of a causal and stable discrete-time system is shown in the figure. The zero at the origin has mu...
GATE ECE 2015 Set 1
For the discrete-time system shown in the figure, the poles of the system transfer function are located at ...
GATE ECE 2015 Set 1
The z-transform of the sequence x$$\left[ n \right]$$ is given by x(z)= $${1 \over {{{(1 - 2{z^{ - 1}})}^2}}}$$ , with t...
GATE ECE 2014 Set 3
Let $${H_1}(z) = {(1 - p{z^{ - 1}})^{ - 1}},{H_2}(z) = {(1 - q{z^{^{ - 1}}})^{ - 1}}$$ , H(z) =$${H_1}(z)$$ +r $${H_2}$$...
GATE ECE 2014 Set 3
The input-output relationship of a causal stable LTI system is given as 𝑦[𝑛] = 𝛼 𝑦[𝑛 − 1] + $$\beta $$ x[n]. If ...
GATE ECE 2014 Set 2
Let x $$\left[ n\right]$$= $${\left( { - {1 \over 9}} \right)^n}\,u(n) - {\left( { - {1 \over 3}} \right)^n}u( - n - 1)....
GATE ECE 2014 Set 1
In the following network (Fig.1), the switch is closed at t = 0 and the sampling starts from t=0. The sampling frequency...
GATE ECE 2008
In the following network (Fig .1), the switch is closed at t = 0- and the sampling starts from t = 0. The sampling frequ...
GATE ECE 2008
The z-transform X (z) f a sequence x$$\left[ n \right]$$ is given by = $${{0.5} \over {1 - 2{z^{ - 1}}}}$$ . It is give...
GATE ECE 2007
The z-transform of a signal is given by c(z)=$${1 \over 4}{{{z^{ - 1}}(1 - {z^{ - 4}})} \over {{{(1 - {z^{ - 1}})}^2}}}$...
GATE ECE 1999
The Z-transform of the following real exponential sequence: x(nT) = $${a^n}$$, nT $$ \ge $$ 0 =0, nT 0 gives us by...
GATE ECE 1990

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