Lecture

Analog Filters: General

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In course

MICRO-310(a): Signals and systems I (for MT)

Présentation des concepts et des outils de base pour la caractérisation des signaux ainsi que pour l'analyse et la synthèse des systèmes linéaires (filtres ou canaux de transmission). Application de ces techniques au traitement du signal et aux télécommuni ...

Description

This lecture covers the synthesis of specific filters, including analog filters, linear phase filters, and rational transfer functions. It discusses the frequency response, step response, and impulse response of analog filters, as well as the classification of analog filters based on causality and phase distortion. Compromises in filter design, frequency specifications, and group propagation time are also explored. The lecture delves into the concept of linear phase filters, their impulse response, and the effects of even and odd symmetry. Additionally, it explains the calculation of impulse response for linear phase filters and the frequency response of real, pure linear phase low-pass filters.

Instructor

Michaël Unser

Expertise Image Processing, Medical Imaging, Biological Imaging, Wavelets, Splines, Multiresolution Michael Unser is Full Professor with EPFL’s school of Engineering and the academic director of EPFL's Center for Imaging, Lausanne, Switzerland. His primary areas of investigation are signal processing, biomedical imaging and applied functional analysis. He is internationally recognized for his research contributions to sampling theory, wavelets, the use of splines for image processing, stochastic processes,

Official source

Ontological neighbourhood

Information engineering

Signal processing: Filtering theory

Related concepts (32)

Filter design

Filter design is the process of designing a signal processing filter that satisfies a set of requirements, some of which may be conflicting. The purpose is to find a realization of the filter that meets each of the requirements to a sufficient degree to make it useful. The filter design process can be described as an optimization problem where each requirement contributes to an error function that should be minimized. Certain parts of the design process can be automated, but normally an experienced electrical engineer is needed to get a good result.

Linear filter

Linear filters process time-varying input signals to produce output signals, subject to the constraint of linearity. In most cases these linear filters are also time invariant (or shift invariant) in which case they can be analyzed exactly using LTI ("linear time-invariant") system theory revealing their transfer functions in the frequency domain and their impulse responses in the time domain. Real-time implementations of such linear signal processing filters in the time domain are inevitably causal, an additional constraint on their transfer functions.

Digital filter

In signal processing, a digital filter is a system that performs mathematical operations on a sampled, discrete-time signal to reduce or enhance certain aspects of that signal. This is in contrast to the other major type of electronic filter, the analog filter, which is typically an electronic circuit operating on continuous-time analog signals. A digital filter system usually consists of an analog-to-digital converter (ADC) to sample the input signal, followed by a microprocessor and some peripheral components such as memory to store data and filter coefficients etc.

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.

Group delay and phase delay

In signal processing, group delay and phase delay are two related ways of describing how a signal's frequency components are delayed in time when passing through a linear time-invariant (LTI) system (such as a microphone, coaxial cable, amplifier, loudspeaker, telecommunications system, ethernet cable, digital filter, or analog filter). Phase delay describes the time shift of a sinusoidal component (a sine wave in steady state).

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