Digital Filtering

A digital filter can be pictured as a "black box" that accepts a sequence of numbers and emits a new sequence of numbers. In digital audio signal processing applications, such number sequences usually represent sounds. For example, digital filters are used to implement graphic equalizers and other digital audio effects. This book is a gentle introduction to digital filters, including mathematical theory, illustrative examples, some audio applications, and useful software starting points. The theory treatment begins at the high-school level, and covers fundamental concepts in linear systems theory and digital filter analysis. Various "small" digital filters are analyzed as examples, particularly those commonly used in audio applications. Matlab programming examples are emphasized for illustrating the use and development of digital filters in practice.

Introduction to digital filters. Finite impulse-response filters. Design of linear-phase finite impulse-response. Minimum-phas and complex approximation. Implementation of finite impulse-response filters. Properties of infinite impulse-response filters. Design of infinite impulse-response filters. Implementation of infinite impulse-response filters. Programs.

This textbook provides an insight into the characteristics and design of digital filters. It includes tables of filter parameters for Butterworth, Chbeyshev, Cauer and Bessel filters and several computer routines for filter design programs.

The order in which the subject matter is presented enables students to make an easy transition from continuous signals and systems to their discrete-time counterparts. A general introduction to terminology and a description of digital filters is followed by a review of continuous filter design. Subsequent chapters deal with sampling theorem and the z-transform; design of recursive digital filters; finite-impulse response and nonrecursive filters; basic concepts in probability theory and random processes; and the methods of design and analysis of the Kalman filter. Contains worked analytical examples, diagrams and problem sets.

Nonlinear Digital Filtering with Python: An Introduction discusses important structural filter classes including the median filter and a number of its extensions (e.g., weighted and recursive median filters), and Volterra filters based on polynomial nonlinearities. Adopting both structural and behavioral approaches in characterizing and designing nonlinear digital filters, this book: Begins with an expedient introduction to programming in the free, open-source computing environment of Python Uses results from algebra and the theory of functional equations to construct and characterize behaviorally defined nonlinear filter classes Analyzes the impact of a range of useful interconnection strategies on filter behavior, providing Python implementations of the presented filters and interconnection strategies Proposes practical, bottom-up strategies for designing more complex and capable filters from simpler components in a way that preserves the key properties of these components Illustrates the behavioral consequences of allowing recursive (i.e., feedback) interconnections in nonlinear digital filters while highlighting a challenging but promising research frontier Nonlinear Digital Filtering with Python: An Introduction supplies essential knowledge useful for developing and implementing data cleaning filters for dynamic data analysis and time-series modeling.

This book has been conceived to extend the generally published work on one- and two-dimensional digital filters in order to include some of the more recently developed ideas. It is intended to supplement and build on the classical books which cover the fundamental concepts of the topic. As a consequence of this, the basic theory is stated in a compact manner and is not developed thoroughly, as this would result in considerable duplication of existing books. The main theme of the book has been to provide a comprehensive background to the methods available for the realization of both recursive and nonrecursive digital filters, and to give an insight into some of the more recent implementation procedures. The book is planned to cover one- and two-dimensional systems in parallel, showing the techniques which are applicable in both areas, and also the limitations and constraints necessary when a one-dimensional technique is extended to systems of higher dimensionality. The theme of the book commences with several chapters on the design of filter transfer functions to meet given specifications. This is followed by a discussion of methods of implementing these in a practical system and the limitations imposed as a result of noise and finite word length. Finally, a discussion of some applications is included.

This textbook provides comprehensive coverage for courses in the basics of design and implementation of digital filters. The book assumes only basic knowledge in digital signal processing and covers state-of-the-art methods for digital filter design and provides a simple route for the readers to design their own filters. The advanced mathematics that is required for the filter design is minimized by providing an extensive MATLAB toolbox with over 300 files. The book presents over 200 design examples with MATLAB code and over 300 problems to be solved by the reader. The students can design and modify the code for their use. The book and the design examples cover almost all known design methods of frequency-selective digital filters as well as some of the authors’ own, unique techniques.