**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.

Concept# Filter (signal processing)

Summary

In signal processing, a filter is a device or process that removes some unwanted components or features from a signal. Filtering is a class of signal processing, the defining feature of filters being the complete or partial suppression of some aspect of the signal. Most often, this means removing some frequencies or frequency bands. However, filters do not exclusively act in the frequency domain; especially in the field of many other targets for filtering exist. Correlations can be removed for certain frequency components and not for others without having to act in the frequency domain. Filters are widely used in electronics and telecommunication, in radio, television, audio recording, radar, control systems, music synthesis, , computer graphics, and structural dynamics.
There are many different bases of classifying filters and these overlap in many different ways; there is no simple hierarchical classification. Filters may be:
*non-linear or linear
*time-variant or time-invariant

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.

Related publications

Loading

Related people

Loading

Related units

Loading

Related concepts

Loading

Related courses

Loading

Related lectures

Loading

Related people (1)

Related concepts (80)

Low-pass filter

A low-pass filter is a filter that passes signals with a frequency lower than a selected cutoff frequency and attenuates signals with frequencies higher than the cutoff frequency. The exact frequency

Electronic filter

Electronic filters are a type of signal processing filter in the form of electrical circuits. This article covers those filters consisting of lumped electronic components, as opposed to distributed

Electronic filter topology

Electronic filter topology defines electronic filter circuits without taking note of the values of the components used but only the manner in which those components are connected.
Filter design cha

Related courses (45)

EE-350: Signal processing

Dans ce cours, nous présentons les méthodes de base du traitement des signaux.

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 of applications for vital sign monitoring and diagnosis purposes.

EE-205: Signals and systems (for EL&IC)

This class teaches the theory of linear time-invariant (LTI) systems. These systems serve both as models of physical reality (such as the wireless channel) and as engineered systems (such as electrical circuits, filters and control strategies).

Related publications (50)

Related units (2)

Loading

Loading

Loading

Nowadays digital signal processing systems used for radar applications, communication systems or RF measurement equipments, require very high sample-rates. Sometimes these sample-rates are beyond the possibilities offered by conventional ADCs. To overcome these limits parallel architectures have been developed. The most commonly used it the one called "time-interleaved" conversion. This technique allows to achieve very-high sample-rates with circuits working at a lower frequency. The accuracy of "time-interleaved" systems is sensitive to sample-time errors. Some calibration techniques have been developed to reduce this sensitivity. They involve very sophisticated digital signal processing and, in most of the cases, they are not directly implemented on silicon but applied on measurement results in software. The goal of this thesis is to study the feasibility of a new parallel architecture for analog-to-digital conversion. This architecture must present a higher robustness to sample-time errors. The first part of this work is dedicated to time-interleaved converter. An analysis of their sensitivity to several imperfections, such as mismatches and systematic and random sample-time error is presented. This analysis is followed by a description of time-interleaved converter evolution, since the first implemented prototype to the current state of the art of the domain. The second part of this thesis focuses on the development of the new conversion technique called "frequency-interleaved". Two different approaches are studied: the first one is based on a Fourier series decomposition of the signal to convert and the second one is based on a Walsh series decomposition. During this study, theoretical and practical aspects are faced the one with the other, to combine signal processing and microelectronics together. It appears that the Fourier series approach offers modest performances and presents serious problems of implementation. Based on this study, the design of functional blocks of a Walsh series based system is proposed.

A fundamental problem in signal processing is to design computationally efficient algorithms to filter signals. In many applications, the signals to filter lie on a sphere. Meaningful examples of data of this kind are weather data on the Earth, or images of the sky. It is then important to design filtering algorithms that are computationally efficient and capable of exploiting the rotational symmetry of the problem. In these applications, given a continuous signal $f: \mathbb S^2 \rightarrow \mathbb R$ on a 2-sphere $\mathbb S^2 \subset \mathbb R^3$, we can only know the vector of its sampled values $\mathbf f \in \mathbb R^N:\ (\mathbf f)_i = f(\mathbf x_i)$ in a finite set of points $\mathcal P \subset \mathbb S^2,\quad \mathcal P = \{\mathbf x_i\}_{i=0}^{n-1}$ where our sensors are located. Perraudin et al. in \cite{DeepSphere} construct a sparse graph $G$ on the vertex set $\mathcal P$ and then use a polynomial of the corresponding graph Laplacian matrix $\mathbf L \in \mathbb R^{n\times n}$ to perform a computationally efficient - $\mathcal O (n)$ - filtering of the sampled signal $\mathbf f$. In order to study how well this algorithm respects the symmetry of the problem - i.e it is equivariant to the rotation group SO(3) - it is important to guarantee that the spectrum of $\mathbf L$ and spectrum of the Laplace-Beltrami operator $\Delta_\mathbb S^2$ are somewhat ``close''. We study the spectral properties of such graph Laplacian matrix in the special case of \cite{DeepSphere} where the sampling $\mathcal P$ is the so called HEALPix sampling (acronym for \textbf Hierarchical \textbf Equal \textbf Area iso\textbf Latitude \textbf {Pix}elization) and we show a way to build a graph $G'$ such that the corresponding graph Laplacian matrix $\mathbf L'$ shows better spectral properties than the one presented in \cite{DeepSphere}. We investigate other different methods of building the matrix $\mathbf L$ better suited to non uniform sampling measures. In particular, we studied the Finite Element Method approximation of the Laplace-Beltrami operator on the sphere, and how FEM filtering relates to graph filtering, showing the importance of non symmetric discrete Laplacians when it comes to non uniform sampling measures. We finish by showing how the graph Laplacian $\mathbf L'$ proposed in this work improved the performances of DeepSphere in a well known classification task using different sampling schemes of the sphere, and by comparing the different Discrete Laplacians introduced in this work.

2019Related lectures (129)