GATE EE 2007 | Linear Time Invariant Systems Question 37 | Signals and Systems

GATE EE 2007

MCQ (Single Correct Answer)

-0.3

Let a signal $${a_1}\,\sin \left( {{\omega _1}t + {\phi _1}} \right)$$ be applied to a stable linear time-invariant system. Let the corresponding steady state output be represented as $${a_2}F\left( {{\omega _2}t + {\phi _2}} \right).$$ Then which of the following statements is true?

$$F$$ is not necessarily a ''sine'' or ''cosine'' function but must be periodic with $${\omega _1} = {\omega _2}.$$

$$F$$ must be a ''sine'' or ''cosine'' function with $${a_1} = {a_2}.$$

$$F$$ must be a ''sine'' function with $${\omega _1} = {\omega _2}.$$ and $${\phi _1} = {\phi _2}.$$

$$F$$ must be a ''sine'' or ''cosine'' function with $${\omega _1} = {\omega _2}.$$

GATE EE 2002

MCQ (Single Correct Answer)

-0.3

$$s(t)$$ is step response and $$h(t)$$ is impulse response of a system. Its response $$y(t)$$ for any input $$u(t)$$ is given by

$${d \over {d\,t}}\int\limits_0^t s \left( {t - \tau } \right)\,u\left( \tau \right)\,d\,\tau $$

$$\int\limits_0^t s \left( {t - \tau } \right)\,u\left( \tau \right)\,d\,\tau $$

$$\int\limits_0^t {\int\limits_0^\tau s \left( {t - {\tau _1}} \right)\,u\left( {{\tau _1}} \right)\,d{\tau _1}} \,d\tau $$

$${d \over {d\,t}}\int\limits_0^t h \left( {t - \tau } \right)\,u\left( \tau \right)\,d\,\tau $$

GATE EE 1994

Subjective

-0

If $$f(t)$$ is the step-response of a linear time-invariant system, then its impulse response is given by ___________

GATE EE 1993

MCQ (Single Correct Answer)

-0.3

$$s(t)$$ is step response and $$h(t)$$ is impulse response of a system. Its response $$y(t)$$ for any input $$u(t)$$ is given by

$${d \over {d\,t}}\int\limits_0^t s \left( {t - \tau } \right)\,u\left( \tau \right)\,d\,\tau $$

$$\int\limits_0^t s \left( {t - \tau } \right)\,u\left( \tau \right)\,d\,\tau $$

$$\int\limits_0^t {\int\limits_0^\tau s \left( {t - {\tau _1}} \right)\,u\left( {{\tau _1}} \right)\,d{\tau _1}} \,d\tau $$

$${d \over {d\,t}}\int\limits_0^t h \left( {t - \tau } \right)\,u\left( \tau \right)\,d\,\tau $$

GATE EE Subjects

Electromagnetic Fields

Time Varying Fields Electrostatics Magnetostatics

Signals and Systems

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

Engineering Mathematics

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

General Aptitude

Verbal Ability Logical Reasoning Numerical Ability

Power Electronics

Choppers and Commutation Techniques Single and Three Phase Rectifier Power Semiconductor Devices Ac Voltage Controllers Inverters

Power System Analysis

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

Analog Electronics

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

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

Digital Electronics

Boolean Algebra Logic Gates Combinational Circuits Minimization Logic Families and Memories Sequential Circuits Analog to Digital and Digital to Analog Converter Microprocessor

Electrical Machines

Induction Machines D.C Machines Synchronous Machines Transformers

Electric Circuits

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

Electrical and Electronics Measurement

Basic of Indicating Instruments Error Analysis and Measurement Measurement of Resistance and A.C Bridges Measurement of Energy and Power Digital Voltmeters Questions Potentiometer and Instrument Transformers Cathode Ray Oscilloscope