Digital Filters Design for Signal and Image Processing

Mohamed Najim

• Publisher: Wiley-ISTE
• Year: 2013
• Print ISBN: 9781905209453
• eBook ISBN: 9781118614686
• Edition: 1
• Topic: Technology & Engineering
• Subtopic: Signals & Signal Processing
• Index: Technology & Engineering

Dealing with digital filtering methods for 1-D and 2-D signals, this book provides the theoretical background in signal processing, covering topics such as the z-transform, Shannon sampling theorem and fast Fourier transform. An entire chapter is devoted to the design of time-continuous filters which provides a useful preliminary step for analog-to-digital filter conversion.
Attention is also given to the main methods of designing finite impulse response (FIR) and infinite impulse response (IIR) filters. Bi-dimensional digital filtering (image filtering) is investigated and a study on stability analysis, a very useful tool when implementing IIR filters, is also carried out. As such, it will provide a practical and useful guide to those engaged in signal processing.

Chapter 1

Introduction to Signals and Systems ¹

1.1. Introduction

Throughout a range of fields as varied as multimedia, telecommunications, geophysics, astrophysics, acoustics and biomedicine, signals and systems play a major role. Their frequential and temporal characteristics are used to extract and analyze the information they contain. However, what importance do signals and systems really hold for these disciplines? In this chapter we will look at some of the answers to this question.

First we will discuss different types of continuous and discrete-time signals, which can be termed random or deterministic according to their nature. We will also introduce several mathematical tools to help characterize these signals. In addition, we will describe the acquisition chain and processing of signals.

Later we will define the concept of a system, emphasizing invariant discrete-time linear systems.

1.2. Signals: categories, representations and characterizations

1.2.1. Definition of continuous-time and discrete-time signals

The function of a signal is to serve as a medium for information. It is a representation of the variations of a physical variable.

A signal can be measured by a sensor, then analyzed to describe a physical phenomenon. This is the situation of a tension taken to the limits of a resistance in order to verify the correct functioning of an electronic board, as well as, to cite one example, speech signals that describe air pressure fluctuations perceived by the human ear.

Generally, a signal is a function of time. There are two kinds of signals: continuous and discrete-time.

A continuous-time or analog signal can be measured at certain instants. This means physical phenomena create, for the most part, continuous-time signals.

Figure 1.1. Example of the sleep spindles of an electroencephalogram (EEG) signal

The advancement of computer-based techniques at the end of the 20^th century led to the development of digital methods for information processing. The capacity to change analog signals to digital signals has meant a continual improvement in processing devices in many application fields. The most significant example of this is in the field of telecommunications, especially in cell phones and digital televisions. The digital representation of signals has led to an explosion of new techniques in other fields as varied as speech processing, audiofrequency signal analysis, biomedical disciplines, seismic measurements, multimedia, radar and measurement instrumentation, among others.

The signal is said to be a discrete-time signal when it can be measured at certain instants; it corresponds to a sequence of numerical values. Sampled signals are the result of sampling, uniform or not, of a continuous-time signal. In this work, we are especially interested in signals taken at regular intervals of time, called sampling periods, which we write as

where f_s is called the sampling rate or the sampling frequency. This is the situation for a temperature taken during an experiment, or of a speech signal (see Figure 1.2). This discrete signal can be written either as x(k) or x(kT_s). Generally, we will use the first writing for its simplicity. In addition, a digital signal is a discrete-time discrete-valued signal. In that case, each signal sample value belongs to a finite set of possible values.

Figure 1.2. Example of a digital voiced speech signal (the sampling frequency f_s is at 16 ...

Table of contents

• Cover
• Title Page
• Copyright
• Introduction
• Chapter 1: Introduction to Signals and Systems
• Chapter 2: Discrete System Analysis
• Chapter 3: Frequential Characterization of Signals and Filters
• Chapter 4: Continuous-Time and Analog Filters
• Chapter 5: Finite Impulse Response Filters
• Chapter 6: Infinite Impulse Response Filters
• Chapter 7: Structures of FIR and IIR Filters
• Chapter 8: Two-Dimensional Linear Filtering
• Chapter 9: Two-Dimensional Finite Impulse Response Filter Design
• Chapter 10: Filter Stability
• Chapter 11: The Two-Dimensional Domain
• List of Authors
• Index