GATE ECE 1998 | Continuous Time Linear Invariant System Question 39 | Signals and Systems

The unit impulse response of a linear time invariant system is the unit step function u(t). For t>0, the response of the system to an excitation e^-at u(t), a>0 will be

a e^-at

(1/a) (1 - e^-at)

a(1 - e^-at)

1 - e^-at)

GATE ECE 1995

MCQ (Single Correct Answer)

-0.3

The transfer function of a linear system is the

ratio of the output, v₀(t), and input, v_i(t).

ratio of the derivatives of the output and the input.

ratio of the Laplace transform of the output and that of the input with all initial conditions zeros.

none of these.

GATE ECE 1995

MCQ (Single Correct Answer)

-0.3

Let h(t) be the impulse response of a linear time invariant system. Then the response of the system for any input u(t) is

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

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

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

$${\int\limits_0^t {{h^2}\left( \tau \right)u\left( {t - \tau } \right)d\tau } }$$

PREVIOUS NEXT

GATE ECE Subjects

Signals and Systems

Representation of Continuous Time Signal Fourier Series Discrete Time Signal Fourier Series Fourier Transform Discrete Time Signal Z Transform Continuous Time Linear Invariant System Transmission of Signal Through Continuous Time LTI Systems Discrete Time Linear Time Invariant Systems Sampling Continuous Time Signal Laplace Transform Discrete Fourier Transform and Fast Fourier Transform Transmission of Signal Through Discrete Time Lti Systems Miscellaneous Fourier Transform

Network Theory

State Equations For Networks Network Elements Network Theorems Two Port Networks Transient Response Sinusoidal Steady State Response Network Graphs Miscellaneous

Control Systems

Basic of Control Systems Signal Flow Graph and Block Diagram Time Response Analysis Stability Root Locus Diagram Frequency Response Analysis Compensators State Space Analysis

Digital Circuits

Number System and Code Convertions Boolean Algebra Logic Gates Combinational Circuits Sequential Circuits Semiconductor Memories Logic Families Analog to Digital and Digital to Analog Converters

General Aptitude

Numerical Ability Logical Reasoning Verbal Ability

Electronic Devices and VLSI

Semiconductor Physics PN Junction BJT and FET IC Basics and MOSFET

Analog Circuits

Diodes Bipolar Junction Transistor Frequency Response FET and MOSFET Oscillators Operational Amplifier Feedback Amplifier Power Amplifier 555 Timer

Engineering Mathematics

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

Microprocessors

Instruction Set and Programming with 8085 Pin Details of 8085 and Interfacing with 8085

Communications

Fundamentals of Information Theory Noise In Digital Communication Analog Communication Systems Digital Communication Systems Random Signals and Noise

Electromagnetics

Waveguides Antennas Miscellaneous Transmission Lines Maxwell Equations Uniform Plane Waves