Digital Filters and Signal Processing

Digital filters, together with signal processing, are being employed in the new technologies and information systems, and are implemented in different areas and applications. Digital filters and signal processing are used with no costs and they can be adapted to different cases with great flexibility and reliability. This book presents advanced developments in digital filters and signal process methods covering different cases studies. They present the main essence of the subject, with the principal approaches to the most recent mathematical models that are being employed worldwide

Digital Filters

The new technology advances provide that a great number of system signals can be easily measured with a low cost. The main problem is that usually only a fraction of the signal is useful for different purposes, for example maintenance, DVD-recorders, computers, electric/electronic circuits, econometric, optimization, etc. Digital filters are the most versatile, practical and effective methods for extracting the information necessary from the signal. They can be dynamic, so they can be automatically or manually adjusted to the external and internal conditions. Presented in this book are the most advanced digital filters including different case studies and the most relevant literature

Generalized linear-in-parameter models : theory and audio signal processing applications

This thesis presents a mathematically oriented perspective to some basic concepts of digital signal processing. A general framework for the development of alternative signal and system representations is attained by defining a generalized linear-in-parameter model (GLM) configuration. The GLM provides a direct view into the origins of many familiar methods in signal processing, implying a variety of generalizations, and it serves as a natural introduction to rational orthonormal model structures. In particular, the conventional division between finite impulse response (FIR) and infinite impulse response (IIR) filtering methods is reconsidered. The latter part of the thesis consists of audio oriented case studies, including loudspeaker equalization, musical instrument body modeling, and room response modeling. The proposed collection of IIR filter design techniques is submitted to challenging modeling tasks. The most important practical contribution of this thesis is the introduction of a procedure for the optimization of rational orthonormal filter structures, called the BU-method. More generally, the BU-method and its variants, including the (complex) warped extension, the (C)WBU-method, can be consider as entirely new IIR filter design strategies.reviewe

Sampled-Data Kalman Filtering and Multiple Model Adaptive Estimation for Infinite-Dimensional Continuous-Time Systems

Kalman filtering and multiple model adaptive estimation (MMAE) methods have been applied by researchers in several engineering disciplines to a multitude of problems featuring a linear (or mildly nonlinear) model based on finite-dimensional differential (or difference) equations perturbed by random inputs. However, many real-world systems are more naturally modeled using an infinite-dimensional continuous-time linear systems model, such as those most naturally modeled as partial differential equations or time-delayed differential equations along with a possibly infinite-dimensional measurement model. The Kalman filtering technique was extended to encompass infinite-dimensional continuous-time systems with sampled-data measurements and a technique to approximate an infinite-dimensional continuous-time system model with an essentially equivalent finite-dimensional discrete-time model upon which a filtering algorithm could be based was developed. The tools developed during this research were demonstrated using an estimation problem based on a stochastic partial differential equation with an unknown noise environment

Multimedia applications of three-dimensional digital filters.

Digital signal processing has long been an extremely important field of study. One-dimensional and two-dimensional filters have applications in areas such as audio filtering or image processing respectively. As VLSI technology continues to increase, higher-dimensional digital filters are becoming more practical. This thesis investigates the application of Three-Dimensional (3-D) Digital Filters to the area of multimedia. Specifically, it investigates the use of 3-D Interpolation filters to increase the horizontal, vertical, and temporal resolution, or frame rate, of a moving image sequence. The thesis begins by presenting the theory of digital interpolation in one dimension, and then extends that theory to three dimensions. Next the theory is presented for the design of a filter with appropriate characteristics for filtering a video image; i.e. near-linear phase and a steep transition band. After the basic theory is presented, a plan for implementing the filtering of a video image in software is presented along with the relevant file format information. Results from this implementation are shown next, and the thesis ends with a summary and conclusions.Dept. of Electrical and Computer Engineering. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis2000 .M34. Source: Masters Abstracts International, Volume: 40-04, page: 1048. Adviser: M. A. Sid-Ahmed. Thesis (M.A.Sc.)--University of Windsor (Canada), 2000

Estimation and control of non-linear and hybrid systems with applications to air-to-air guidance

Issued as Progress report, and Final report, Project no. E-21-67

Structure-Preserving Model Reduction of Physical Network Systems

This paper considers physical network systems where the energy storage is naturally associated to the nodes of the graph, while the edges of the graph correspond to static couplings. The first sections deal with the linear case, covering examples such as mass-damper and hydraulic systems, which have a structure that is similar to symmetric consensus dynamics. The last section is concerned with a specific class of nonlinear physical network systems; namely detailed-balanced chemical reaction networks governed by mass action kinetics. In both cases, linear and nonlinear, the structure of the dynamics is similar, and is based on a weighted Laplacian matrix, together with an energy function capturing the energy storage at the nodes. We discuss two methods for structure-preserving model reduction. The first one is clustering; aggregating the nodes of the underlying graph to obtain a reduced graph. The second approach is based on neglecting the energy storage at some of the nodes, and subsequently eliminating those nodes (called Kron reduction).</p

Smoothness assumptions in human and machine vision, and their implications for optimal surface interpolation

In this paper we shall examine what smoothness assumptions are made about object surfaces, object motion, and image intensities. We begin by looking into the physiological limits of vision and how these might influence our perception of smoothness. We then look at a sampling of the computer vision and psychology literature, inferring smoothness constraints from the mathematical assumptions tacitly presumed by researchers. This look at computer vision and psychology of vision is not meant to be an inclusive study, but rather representative of the assumptions made, and in part representative of the mathematical models used therein. We shall conclude that prevalent assumptions are that surfaces, motion, and intensity images are functions in C2, eland c2 respectively. In the latter portion of this paper we examine one use of explicit assumptions on smoothness in the definition of existing method for obtaining "optimal" surface interpolation. We briefly introduce the nomenclature of information-based complexity originated by Traub, Wozniakowski, and their colleagues, which is the mathematical machinery used in obtaining these "optimal" surfaces. This theory requires that we know the class of functions from which our desired surface comes, and part of the definition of a class is the degree of smoothness. We then survey many possible classes for the visual interpolation problem of two dimensional surfaces, and state formulas from which one can obtain the optimal surface interpolating given depth data