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

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

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

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

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

GATE EE Subjects

Electric Circuits

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

Electromagnetic Fields

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

Induction Machines D.C Machines Synchronous Machines Transformers

Engineering Mathematics

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

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Parameters and Performance of Transmission Lines Power Generation Cost Power System Stability Symmetrical Components and Symmetrical and Unsymmetrical Faults Circuit Breaker Switch Gear and Protection Per Unit System Load Flow Studies High Voltage Dc Transmission Generating Power Station

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Diode Circuits and Applications Bjt and Mosfet Biasing Small Signal Modeling Feedback Amplifiers and Oscillator Circuits Operational Amplifier Frequency Response 555 Timer

Control Systems

Block Diagram and Signal Flow Graph Polar Nyquist and Bode Plot State Variable Analysis Basics of Control System Routh Hurwitz Stability Time Response Analysis Root Locus Techniques Controller and Compensator

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