Digital Signal Processing

Concepts and Applications

Bernard Mulgrew, Peter Grant, John Thompson

• Publisher: Bloomsbury Academic
• Year: 2002
• Print ISBN: 9780333963562
• eBook ISBN: 9781350306356
• Edition: 2
• Topic: Technology & Engineering
• Subtopic: Electrical Engineering & Telecommunications
• Index: Technology & Engineering

Digital Signal Processing: Concepts and Applications, second edition covers the basic principles and operation of DSP devices. Its aim is to give the student the essentials of this mathematical subject in a form that can be easily understood and assimilated. The text concentrates on discrete systems, starting from digital filters and discrete Fourier transforms. These are then extended into adaptive filters and spectrum analysers with the minimum of mathematical derivation, concentrating on demonstrating the performance which is achievable from these processors in communications and radar system applications. This new edition has been updated to include learning outcomes and summaries and provide more examples. The text has been completely redesigned and is presented in a clear and easy-to-read style.

Key features:
- Self assessment questions within the text, with answers provided
- Numerous practical worked examples on processor design and performance simulation
- MATLAB® code for animated simulations available to students via World Wide Web access

This textbook is appropriate for undergraduate and MSc courses in signals and systems and signal processing, and for professional engineers who wish to have a simple, easy-to-read reference book on DSP techniques.

CHAPTER 1

Signal representation and system response

CHAPTER INTRODUCTION

In this chapter the concept of a signal and a system to which that signal is applied are introduced through an example. The issue of signal classification is discussed with consideration given to periodic, non-periodic, finite energy and finite power classes. While the simplest representation of a periodic signal is as a function of time (time-domain description), frequency domain representations such as trigonometric and complex Fourier series can also be extremely useful – these are introduced and discussed. These frequency-domain representations lead naturally to the Fourier transform to handle non-periodic signals. In turn some of the technical difficulties with the Fourier transform lead to the Laplace transform. These alternative representations of signals are in fact variations on a theme in that they describe the original time-domain signal as a weighted sum (or integral) of complex phasors. The concepts of transform representation, superposition and easy methods for calculating the response of linear equations to complex phasors are drawn together to highlight the intimate link between such transform representations and the analysis of the response of linear systems to a wide range of input signals. A brief review of the widely used Laplace transform method for calculating the response of a linear system to a given input is provided.

The learning objectives of this chapter are to:

•become familiar with the concepts of a signal and the concept of a system;

•understand how the Fourier series is used to represent periodic signals;

•understand how the Fourier and Laplace transform are used to represent a more general class of signals;

•recognise the common ingredients in these series and transforms;

•understand the role of these transforms in evaluating the response of a linear system to a particular signal.

1.1.Signals and systems?

Perhaps the most familiar example of a signal is a musical sound. Plucking a string on a guitar causes that string to vibrate up and down as illustrated in Figure 1.1(a). Plotting the vertical position of one point on the string as a function, x(), of time, t, reveals the periodic motion of the string (Figure 1.1(b)). The motion of the string alters the pressure in the air around the string and the pressure of the air will oscillate in sympathy with the movement of the string. The pressure wave radiates from the guitar towards the microphone which converts the fluctuations in pressure to an electrical voltage oscillation (Figure 1.2(a)). All of these oscillations are examples of signals. All of them carry information. Listening to a recording of the electrical signal, most people would be able to identify the instrument being played, i.e. would be able to distinguish between a guitar and a piano. Some people might be able to identify the pitch and hence the note being played.

When the string is plucked, the pressure wave radiates out from the string in all directions. There are many paths that it can take from the string to the microphone. For example, there is a direct or line of sight (LOS) path from the string to the microphone; there is also a path from the front of the guitar, reflecting off a wall to the microphone. Since the speed of sound in air is approximately constant and the lengths of the paths are different, the signal from the guitar will reach the microphone at different times. These delayed versions of the signal will interfere constructively and destructive...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright
• Contents
• Preface
• Acknowledgements
• Abbreviations
• Advertisement
• Abstract
• Introduction
• 1 Signal representation and system response
• 2 Time-domain description and convolution
• 3 Transfer function and system characterisation
• 4 Sampled data systems and the z-transform
• 5 Infinite impulse response digital filters
• 6 Finite impulse response digital filters
• 7 Analysis of random signals
• 8 Adaptive filters
• 9 The Fourier transform and spectral analysis
• 10 The fast Fourier transform
• 11 Multirate signal processing
• Appendix A – Matrix theory revision
• Appendix B – Signal transforms
• Solutions to self assessment questions
• Digital Signal Processing bibliography
• Index