**Êtes-vous un étudiant de l'EPFL à la recherche d'un projet de semestre?**

Travaillez avec nous sur des projets en science des données et en visualisation, et déployez votre projet sous forme d'application sur Graph Search.

Concept# Time–frequency analysis

Résumé

In signal processing, time–frequency analysis comprises those techniques that study a signal in both the time and frequency domains simultaneously, using various time–frequency representations. Rather than viewing a 1-dimensional signal (a function, real or complex-valued, whose domain is the real line) and some transform (another function whose domain is the real line, obtained from the original via some transform), time–frequency analysis studies a two-dimensional signal – a function whose domain is the two-dimensional real plane, obtained from the signal via a time–frequency transform.
The mathematical motivation for this study is that functions and their transform representation are tightly connected, and they can be understood better by studying them jointly, as a two-dimensional object, rather than separately. A simple example is that the 4-fold periodicity of the Fourier transform – and the fact that two-fold Fourier transform reverses direction – can be interpreted by considering the Fourier transform as a 90° rotation in the associated time–frequency plane: 4 such rotations yield the identity, and 2 such rotations simply reverse direction (reflection through the origin).
The practical motivation for time–frequency analysis is that classical Fourier analysis assumes that signals are infinite in time or periodic, while many signals in practice are of short duration, and change substantially over their duration. For example, traditional musical instruments do not produce infinite duration sinusoids, but instead begin with an attack, then gradually decay. This is poorly represented by traditional methods, which motivates time–frequency analysis.
One of the most basic forms of time–frequency analysis is the short-time Fourier transform (STFT), but more sophisticated techniques have been developed, notably wavelets and least-squares spectral analysis methods for unevenly spaced data.
In signal processing, time–frequency analysis is a body of techniques and methods used for characterizing and manipulating signals whose statistics vary in time, such as transient signals.

Source officielle

Cette page est générée automatiquement et peut contenir des informations qui ne sont pas correctes, complètes, à jour ou pertinentes par rapport à votre recherche. Il en va de même pour toutes les autres pages de ce site. Veillez à vérifier les informations auprès des sources officielles de l'EPFL.

Cours associés (31)

Personnes associées (53)

Concepts associés (16)

MOOCs associés (8)

Séances de cours associées (156)

Publications associées (524)

Unités associées (7)

Proximité ontologique

EE-548: Audio engineering

This lecture is oriented towards the study of audio engineering, with a special focus on room acoustics applications. The learning outcomes will be the techniques for microphones and loudspeaker desig

ME-221: Dynamical systems

Provides the students with basic notions and tools for the analysis of dynamic systems. Shows them how to develop mathematical models of dynamic systems and perform analysis in time and frequency doma

EE-512: Applied biomedical signal processing

The goal of this course is twofold: (1) to introduce physiological basis, signal acquisition solutions (sensors) and state-of-the-art signal processing techniques, and (2) to propose concrete examples

Wavelet transform

In mathematics, a wavelet series is a representation of a square-integrable (real- or complex-valued) function by a certain orthonormal series generated by a wavelet. This article provides a formal, mathematical definition of an orthonormal wavelet and of the integral wavelet transform. A function is called an orthonormal wavelet if it can be used to define a Hilbert basis, that is a complete orthonormal system, for the Hilbert space of square integrable functions.

Bandlimiting

Bandlimiting refers to a process which reduces the energy of a signal to an acceptably low level outside of a desired frequency range. Bandlimiting is an essential part of many applications in signal processing and communications. Examples include controlling interference between radio frequency communications signals, and managing aliasing distortion associated with sampling for digital signal processing. A bandlimited signal is, strictly speaking, a signal with zero energy outside of a defined frequency range.

Time–frequency representation

A time–frequency representation (TFR) is a view of a signal (taken to be a function of time) represented over both time and frequency. Time–frequency analysis means analysis into the time–frequency domain provided by a TFR. This is achieved by using a formulation often called "Time–Frequency Distribution", abbreviated as TFD. TFRs are often complex-valued fields over time and frequency, where the modulus of the field represents either amplitude or "energy density" (the concentration of the root mean square over time and frequency), and the argument of the field represents phase.

Digital Signal Processing [retired]

The course provides a comprehensive overview of digital signal processing theory, covering discrete time, Fourier analysis, filter design, sampling, interpolation and quantization; it also includes a

Digital Signal Processing

Digital Signal Processing is the branch of engineering that, in the space of just a few decades, has enabled unprecedented levels of interpersonal communication and of on-demand entertainment. By rewo

Digital Signal Processing I

Basic signal processing concepts, Fourier analysis and filters. This module can
be used as a starting point or a basic refresher in elementary DSP

Transformée Fourier

Couvre la transformée de Fourier, essentielle pour analyser des systèmes LTI stables à travers des exponentielles complexes.

Fourier Transform: Bases

Couvre les bases de Fourier Transform et ses applications dans le traitement des signaux.

Signaux & Systèmes I: Pondération des Fenêtres et Phénomène de Gibbs

Explore les fenêtres de pondération, le phénomène Gibbs, la série Fourier et la limitation de fréquence dans les signaux et les systèmes.

Modern power distribution systems are experiencing a large-scale integration of Converter-Interfaced Distributed Energy Resources (CIDERs). Their presence complicates the analysis and mitigation of harmonics, whose creation and propagation may be amplified ...

Situational awareness strategies are essential for the reliable and secure operation of the electric power grid which represents critical infrastructure in modern society. With the rise of converter-interfaced renewable generation and the consequent shift ...

Alireza Karimi, Elias Sebastian Klauser

In this paper, the challenge of asymptotically rejecting sinusoidal disturbances with unknown time-varying frequency and bounded rate is explored. A novel data-driven approach for designing linear parameter-varying (LPV) con- troller is introduced, leverag ...

2024