**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# Linear Phase Filters: Theory and Design

Description

This lecture covers the theory and design of linear phase filters, discussing concepts such as group propagation time, polar form of the frequency response, differential formula for group delay, and the necessary conditions for achieving linear phase filters. It also explores the synthesis of digital filters, Chebyshev criterion, and the placement of poles and zeros. The lecture emphasizes the importance of achieving linear phase clamps and symmetrical linear phase filters for optimal filter performance.

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

Related concepts (32)

Instructor

MICRO-311(b): Signals and systems II (for SV)

Ce cours aborde la théorie des systèmes linéaires discrets invariants par décalage (LID). Leurs propriétés et caractéristiques fondamentales y sont discutées, ainsi que les outils fondamentaux permett

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-element filters. That is, using components and interconnections that, in analysis, can be considered to exist at a single point. These components can be in discrete packages or part of an integrated circuit. Electronic filters remove unwanted frequency components from the applied signal, enhance wanted ones, or both.

Filter (signal processing)

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.

Digital biquad filter

In signal processing, a digital biquad filter is a second order recursive linear filter, containing two poles and two zeros. "Biquad" is an abbreviation of "biquadratic", which refers to the fact that in the Z domain, its transfer function is the ratio of two quadratic functions: The coefficients are often normalized such that a0 = 1: High-order infinite impulse response filters can be highly sensitive to quantization of their coefficients, and can easily become unstable.

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.

Related lectures (38)

Digital Filters: Implementation and AnalysisMICRO-311(b): Signals and systems II (for SV)

Explores digital filters' implementation, cyclic convolution, FFT-based filtering, and the importance of filtering in signal processing.

RIF Filters: Characteristics and SynthesisEE-350: Signal processing

Explores the characteristics and synthesis of RIF filters, including windowing operations and linear phase filters.

Active Filters: Second-order and High-order RealizationsMICRO-211: Analog circuits and systems

Covers the design and implementation of active filters, focusing on second-order and high-order realizations.

Digital Filtering: Butterworth Filter DesignME-324: Discrete-time control of dynamical systems

Explores digital Butterworth filter design, covering scaling, stable poles, and filter application.

The convolution theoremMOOC: Digital Signal Processing I

Explores the convolution theorem, DTFT reconstruction, frequency response effects, and signal building.