Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Lecture

Signals and Systems: Time Shift and Reflection

In course

MICRO-310(b): Signals and systems I (for SV)

Présentation des concepts et des outils de base pour l'analyse et la caractérisation des signaux, la conception de systèmes de traitement et la modélisation linéaire de systèmes pour les étudiants en sciences de la vie. Application de ces techniques au tra ...

Description

This lecture covers the interpretation of time shift, reflection, area calculation, response of a system, convolution, elementary excitations, impulse responses, differentiation operators, homogeneous solutions, differential equations, characteristic polynomial, green function, inverse operator, RC circuit example, linear differential equations, system response, zero excitation, and characteristic modes. It emphasizes the factorization of differential operators, characteristic modes, and the importance of specifying initial conditions for a unique solution.

This video is available exclusively on Mediaspace for a restricted audience. Please log in to MediaSpace to access it if you have the necessary permissions.

Watch on Mediaspace

Instructor

Michaël Unser

Official source

Ontological neighbourhood

Mathematics

Analysis: Differential anaysis

Related concepts (32)

Homogeneous differential equation

A differential equation can be homogeneous in either of two respects. A first order differential equation is said to be homogeneous if it may be written where f and g are homogeneous functions of the same degree of x and y. In this case, the change of variable y = ux leads to an equation of the form which is easy to solve by integration of the two members. Otherwise, a differential equation is homogeneous if it is a homogeneous function of the unknown function and its derivatives.

Ordinary differential equation

In mathematics, an ordinary differential equation (ODE) is a differential equation (DE) dependent on only a single independent variable. As with other DE, its unknown(s) consists of one (or more) function(s) and involves the derivatives of those functions. The term "ordinary" is used in contrast with partial differential equations which may be with respect to one independent variable. A linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form where a_0(x), .

Delay differential equation

In mathematics, delay differential equations (DDEs) are a type of differential equation in which the derivative of the unknown function at a certain time is given in terms of the values of the function at previous times. DDEs are also called time-delay systems, systems with aftereffect or dead-time, hereditary systems, equations with deviating argument, or differential-difference equations. They belong to the class of systems with the functional state, i.e.

Partial differential equation

In mathematics, a partial differential equation (PDE) is an equation which computes a function between various partial derivatives of a multivariable function. The function is often thought of as an "unknown" to be solved for, similar to how x is thought of as an unknown number to be solved for in an algebraic equation like x2 − 3x + 2 = 0. However, it is usually impossible to write down explicit formulas for solutions of partial differential equations.

Stochastic differential equation

A stochastic differential equation (SDE) is a differential equation in which one or more of the terms is a stochastic process, resulting in a solution which is also a stochastic process. SDEs have many applications throughout pure mathematics and are used to model various behaviours of stochastic models such as stock prices, random growth models or physical systems that are subjected to thermal fluctuations. SDEs have a random differential that is in the most basic case random white noise calculated as the derivative of a Brownian motion or more generally a semimartingale.

Related lectures (37)

Canonical Transformations: Existence and Equations

Explores canonical transformations, focusing on existence, equations, simplicity, and differential equations' theory.

Convolution and Laplace Transform

Explores control of dynamic systems, impulse response, Laplace transform, and Fourier transform for solving differential equations.

Homogeneous Linear Second-Order Differential Equations

Covers the solution of homogeneous linear second-order differential equations with constant coefficients and explores various cases of real and complex roots.

Linear Differential Equations Log in to Mediaspace to watch this video

Explores solving linear differential equations and the principle of superposition with illustrative examples.

Principle of Superposition in Differential Equations Log in to Mediaspace to watch this video