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Signals and Systems
Linear Time Invariant Systems
Marks 1Marks 2Marks 4Marks 5
Continuous and Discrete Time Signals
Marks 1Marks 2
Continuous Time Signal Fourier Transform
Marks 1Marks 2
Continuous Time Periodic Signal Fourier Series
Marks 1Marks 2Marks 5
Discrete Time Signal Z Transformation
Marks 1Marks 2
Miscellaneous
Marks 2
Continuous Time Signal Laplace Transform
Marks 1Marks 2
Sampling Theorem
Marks 1Marks 2
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1
GATE EE 2024
MCQ (Single Correct Answer)
+2
-1.33

If the Z-transform of a finite-duration discrete-time signal $x[n]$ is $X(z)$, then the Z-transform of the signal $y[n] = x[2n]$ is

A

$Y(z) = X(z^2)$

B

$Y(z) = \frac{1}{2} \left[ X(z^{-1/2}) + X(-z^{-1/2}) \right]$

C

$Y(z) = \frac{1}{2} \left[ X(z^{1/2}) + X(-z^{1/2}) \right]$

D

$Y(z) = \frac{1}{2} \left[ X(z^2) + X(-z^2) \right]$

2
GATE EE 2023
Numerical
+2
-0

The discrete-time Fourier transform of a signal $$x[n]$$ is $$X(\Omega ) = (1 + \cos \Omega ){e^{ - j\Omega }}$$. Consider that $${x_p}[n]$$ is a periodic signal of period N = 5 such that

$${x_p}[n] = x[n]$$, for $$n = 0,1,2$$

= 0, for $$n = 3,4$$

Note that $${x_p}[n] = \sum\nolimits\limits_{k = 0}^{n - 1} {{a_k}{e^{j{{2\pi } \over N}kn}}} $$. The magnitude of the Fourier series coeffiient $$a_3$$ is __________ (Round off to 3 decimal places).

Your input ____
3
GATE EE 2017 Set 2
MCQ (Single Correct Answer)
+2
-0.6
A cascade system having the impulse responses $$$\begin{array}{l}h_1\left(n\right)=\left\{1,\;-1\right\}\;\;\;and\;\;h_2\left(n\right)=\left\{1,\;1\right\}\\\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\uparrow\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\uparrow\end{array}$$$ is shown in the figure below, where symbol $$\uparrow$$ denotes the time origin. GATE EE 2017 Set 2 Signals and Systems - Discrete Time Signal Z Transformation Question 10 English The input sequence x(n) for which the cascade system produces an output sequence $$$\begin{array}{l}y\left(n\right)=\left\{1,\;2,\;1,\;-1,\;-2,\;-1\right\}\;\;is\\\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\uparrow\end{array}$$$
A
$$\begin{array}{l}x\left(n\right)=\left\{1,\;2,\;1,\;1\right\}\\\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\uparrow\end{array}$$
B
$$\begin{array}{l}x\left(n\right)=\left\{1,\;1,\;2,\;2\right\}\\\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\uparrow\end{array}$$
C
$$\begin{array}{l}x\left(n\right)=\left\{1,\;1,\;1\right\}\\\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\uparrow\end{array}$$
D
$$\begin{array}{l}x\left(n\right)=\left\{1,\;2,\;2,\;1\right\}\\\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\uparrow\end{array}$$
4
GATE EE 2015 Set 1
MCQ (Single Correct Answer)
+2
-0.6
Consider a discrete time signal given by
x[n]=(-0.25)nu[n]+(0.5)nu[-n-1]
The region of convergence of its Z-transform would be
A
the region inside the circle of radius 0.5 and centered at origin.
B
the region outside the circle of radius 0.25 and centered at origin.
C
the annular region between the two circles, both centered at origin and having radii 0.25 and 0.5.
D
the entire Z plane.
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Questions Asked from Marks 2
GATE EE 2024 (1) GATE EE 2023 (1) GATE EE 2017 Set 2 (1) GATE EE 2015 Set 1 (1) GATE EE 2014 Set 2 (1) GATE EE 2014 Set 1 (1) GATE EE 2008 (1) GATE EE 2006 (1) GATE EE 2005 (1)
GATE EE Subjects
Electromagnetic Fields
Signals and Systems
Engineering Mathematics
General Aptitude
Power Electronics
Power System Analysis
Analog Electronics
Control Systems
Digital Electronics
Electrical Machines
Electric Circuits
Electrical and Electronics Measurement