# Discrete Time Signal Z Transform · Signals and Systems · GATE ECE

Start Practice## Marks 1

GATE ECE 2018

A discrete time all-pass system has two of its poles at
0.25$$\angle 0^\circ $$ and $$\angle 30^\circ $$. Which one of the following statements about ...

GATE ECE 2016 Set 3

A discrete-time signal$$x\left[ n \right]\, = \delta \left[ {n - 3} \right]\, + 2\delta \left[ {n - 5} \right]$$ has z-transform x(z). If Y (z)=X (-z)...

GATE ECE 2016 Set 1

Consider the sequence
$$x\left[ n \right]$$= $${a^n}u\left[ n \right] + {b^{\partial n}}u\left[ n \right]$$ , where u[n] denotes the unit step seque...

GATE ECE 2015 Set 2

Two casual discrete-time signals $$x\left[ n \right]$$ and $$y\left[ n \right]$$ =$$\sum\limits_{m = 0}^n x \left[ m \right]$$. If the z-transform of ...

GATE ECE 2014 Set 4

The sequence x $$\left[ n \right]$$ = $${0.5^n}$$ u[n], where u$$\left[ n \right]$$ is the unit step sequence, is convolved with itself to obtain y ...

GATE ECE 2014 Set 3

For an all-pass system H(z)= $${{({z^{ - 1}} - b)} \over {(1 - a{z^{ - 1}})}}$$ where $$\left| {H({e^{ - j\omega }})} \right| = \,1$$ , for all $$\o...

GATE ECE 2014 Set 2

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 0.25 is a zero of X(z), which one...

GATE ECE 2012

If $$x\left[ n \right]$$= $${(1/3)^{\left| n \right|}} - {(1/2)^n}u\left[ n \right]$$, then the region of convergence (ROC) of its Z- transform in th...

GATE ECE 2010

Consider the z-transform
X(z)=5$${z^2} + 4{z^{ - 1}} + 3;0 < \left| z \right| < \infty $$.
The inverse z - transform x$$\,\left[ n \right]$$ i...

GATE ECE 2009

The ROC of Z-transform of the discrete time sequence
x(n)= $${\left( {{1 \over 3}} \right)^{n}}u(n) - {\left( {{1 \over 2}} \right)^{ n}}\,u( - n - 1...

GATE ECE 2006

If the region of convergence of $${x_1}\left[ n \right]$$ + $${x_2}\left[ n \right]$$ is 1/3< $$\left| {z\,} \right|$$<2/3, then the region of ...

GATE ECE 2005

The region of convergence of z-transform of the sequence $${\left( {{5 \over 6}} \right)^n}u(n) - {\left( {{6 \over 5}} \right)^n}u( - n - 1)$$ must ...

GATE ECE 2004

The z transform of a system is
H(z) = $${z \over {z - 0.2}}$$ .
If the ROC is $$\left| {z\,} \right|$$ < 0.2, then the impulse response of the s...

GATE ECE 2001

The region of convergence of the z- transform of a unit step function is

GATE ECE 1999

The z-transform F(z) of the function f(nT) = $${a^{nT}}$$ is

GATE ECE 1998

The z - transform of the time function $$\sum\limits_{k = 0}^\infty {\delta \left( {n - k} \right)} $$ is

## Marks 2

GATE ECE 2016 Set 3

The ROC (region of convergence) of the z-transform of a discrete-time signal is represented by the shaded
region in the z-plane. If the signal $$x\lef...

GATE ECE 2016 Set 1

A sequence x$$\left[ n \right]$$ is specified as $$\left[ {\matrix{
{x\left[ n \right]} \cr
{x\left[ {n - 1} \right]} \cr
} } \right] = {\...

GATE ECE 2015 Set 3

A realization of a stable discrete time system is shown in the figure. If the system is excited by a
unit step sequence input x[n ] , the response y[...

GATE ECE 2015 Set 3

Suppose x $$\left[ n \right]$$ is an absolutely summable discrete-time signal. Its z-transform is a rational function
with two poles and two zeroes. T...

GATE ECE 2015 Set 1

The pole-zero diagram of a causal and stable discrete-time system is shown in the figure. The zero at the origin has
multiplicity 4. The impulse resp...

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 2014 Set 3

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 $$\le...

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 $${H_2}$$. The quantities p, q, r are r...

GATE ECE 2014 Set 2

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 t...

GATE ECE 2014 Set 1

Let x $$\left[ n\right]$$= $${\left( { - {1 \over 9}} \right)^n}\,u(n) - {\left( { - {1 \over 3}} \right)^n}u( - n - 1).$$ The region of Convergence (...

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 frequency is 10 Hz.
The expressio...

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 frequency is 10 Hz.
The samples x (n)...

GATE ECE 2007

The z-transform X (z) f a sequence x$$\left[ n \right]$$ is given by = $${{0.5} \over {1 - 2{z^{ - 1}}}}$$ . It is given that the region of convergen...

GATE ECE 1999

The z-transform of a signal is given by c(z)=$${1 \over 4}{{{z^{ - 1}}(1 - {z^{ - 4}})} \over {{{(1 - {z^{ - 1}})}^2}}}$$. Its final value is

GATE ECE 1990

The Z-transform of the following real exponential sequence:
x(nT) = $${a^n}$$, nT $$ \ge $$ 0
=0, nT<0, a> 0
gives us by