GATE EE 2023 | Discrete Time Signal Z Transformation Question 2 | Signals and Systems

GATE EE 2023

MCQ (Single Correct Answer)

-0.33

The Z-transform of a discrete signal $$x[n]$$ is

$$X(z) = {{4z} \over {(z - {1 \over 5})(z - {2 \over 3})(z - 3)}}$$ with $$ROC = R$$.

Which one of the following statements is true?

Discrete-time Fourier transform of $$x[n]$$ converges if R is $$|z| > 3$$

Discrete-time Fourier transform of $$x[n]$$ converges if R is $${2 \over 3} < |z| < 3$$

Discrete-time Fourier transform of $$x[n]$$ converges if R is such that $$x[n]$$ is a left-sided sequence

Discrete-time Fourier transform of $$x[n]$$ converges if R is such that $$x[n]$$ is a right-sided sequence

GATE EE 2017 Set 2

MCQ (Single Correct Answer)

-0.3

The pole-zero plots of three discrete-time systems P, Q and R on the z-plane are shown below. GATE EE 2017 Set 2 Signals and Systems - Discrete Time Signal Z Transformation Question 12 English

GATE EE 2017 Set 2 Signals and Systems - Discrete Time Signal Z Transformation Question 12 English

Which one of the following is TRUE about the frequency selectivity of these systems?

All three are high-pass filters.

All three are band-pass filters.

All three are low-pass filters.

P is a low-pass filter, Q is a band-pass filter and R is a high-pass filter.

GATE EE 2015 Set 2

MCQ (Single Correct Answer)

-0.3

The z-Transform of a sequence x[n] is given as X(z) = 2z+4−4/z+3/z². If y[n] is the first difference of x[n], then Y(Z) is given by

$$2z+2-\frac8z+\frac7{z^2}-\frac3{z^3}$$

$$-2z+2-\frac6z+\frac1{z^2}-\frac3{z^3}$$

$$-2z-2+\frac8z-\frac7{z^2}+\frac3{z^3}$$

$$4z-2-\frac8z-\frac1{z^2}+\frac3{z^3}$$

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Electric Circuits

Network Elements Network Theorems Three Phase Circuits Transient Response Sinusoidal Steady State Analysis Graph Theory Two Port Networks

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Time Varying Fields Electrostatics Magnetostatics

Signals and Systems

Linear Time Invariant Systems Continuous and Discrete Time Signals Continuous Time Signal Fourier Transform Continuous Time Periodic Signal Fourier Series Discrete Time Signal Z Transformation Miscellaneous Continuous Time Signal Laplace Transform Sampling Theorem

Electrical Machines

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Engineering Mathematics

Linear Algebra Differential Equations Calculus Probability and Statistics Numerical Methods Vector Calculus Transform Theory Complex Variable

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