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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