**Are you an EPFL student looking for a semester project?**

Work with us on data science and visualisation projects, and deploy your project as an app on top of GraphSearch.

Lecture# LTI Systems and the Laplace Transform

Description

This lecture covers the concept of LTI systems and the Laplace Transform, explaining the transfer function, convolution, impulse response, frequency response, and system properties like stability and causality.

Official source

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

In course

Instructors (2)

EE-205: Signals and systems (for EL)

Ce cours pose les bases d'un concept essentiel en ingénierie : la notion de système. Plus spécifiquement, le cours présente la théorie des systèmes linéaires invariants dans le temps (SLIT), qui sont

Related concepts (32)

Step response

The step response of a system in a given initial state consists of the time evolution of its outputs when its control inputs are Heaviside step functions. In electronic engineering and control theory, step response is the time behaviour of the outputs of a general system when its inputs change from zero to one in a very short time. The concept can be extended to the abstract mathematical notion of a dynamical system using an evolution parameter.

Frequency response

In signal processing and electronics, the frequency response of a system is the quantitative measure of the magnitude and phase of the output as a function of input frequency. The frequency response is widely used in the design and analysis of systems, such as audio and control systems, where they simplify mathematical analysis by converting governing differential equations into algebraic equations.

Impulse response

In signal processing and control theory, the impulse response, or impulse response function (IRF), of a dynamic system is its output when presented with a brief input signal, called an impulse (δ(t)). More generally, an impulse response is the reaction of any dynamic system in response to some external change. In both cases, the impulse response describes the reaction of the system as a function of time (or possibly as a function of some other independent variable that parameterizes the dynamic behavior of the system).

Linear time-invariant system

In system analysis, among other fields of study, a linear time-invariant (LTI) system is a system that produces an output signal from any input signal subject to the constraints of linearity and time-invariance; these terms are briefly defined below. These properties apply (exactly or approximately) to many important physical systems, in which case the response y(t) of the system to an arbitrary input x(t) can be found directly using convolution: y(t) = (x ∗ h)(t) where h(t) is called the system's impulse response and ∗ represents convolution (not to be confused with multiplication).

Infinite impulse response

Infinite impulse response (IIR) is a property applying to many linear time-invariant systems that are distinguished by having an impulse response which does not become exactly zero past a certain point, but continues indefinitely. This is in contrast to a finite impulse response (FIR) system in which the impulse response does become exactly zero at times for some finite , thus being of finite duration. Common examples of linear time-invariant systems are most electronic and digital filters.

Related lectures (35)

Sampling Theorem and Control SystemsME-326: Control systems and discrete-time control

Explores the Sampling Theorem, digital control, signal reconstruction, and anti-aliasing filters.

Laplace Transform Application: LTI SystemsEE-205: Signals and systems (for EL)

Covers the application of Laplace transform to LTI Systems, including examples and differential equations.

Frequency Response of LTI SystemsEE-205: Signals and systems (for EL)

Explores LTI systems, impulse response, convolution, system properties, and frequency response, including low-pass and band-pass filters.

Signals & Systems II: Roots, Equations, and Impulse ResponsesMICRO-311(a): Signals and systems II (for MT)

Explores roots verification, stability, reproduction modeling, Z transform, and LTI systems realization.

Signals & Systems ReviewEE-205: Signals and systems (for EL)

Provides a comprehensive review of signals and systems, covering topics such as time-domain analysis, frequency-domain analysis, and Fourier transform.