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Appendix A: Some useful Laplace and z-transforms
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Appendix A: Some useful Laplace and z-transforms
by Robert Meddins
Introduction to Digital Signal Processing
Cover image
Title page
Table of Contents
Copyright
Series Preface
Dedication
Preface
Acknowledgements
Chapter 1: The basics
1.1 CHAPTER PREVIEW
1.2 ANALOGUE SIGNAL PROCESSING
1.3 AN ALTERNATIVE APPROACH
1.4 THE COMPLETE DSP SYSTEM
1.5 RECAP
1.6 DIGITAL DATA PROCESSING
1.7 THE RUNNING AVERAGE FILTER
1.8 REPRESENTATION OF PROCESSING SYSTEMS
1.9 SELF-ASSESSMENT TEST
1.10 FEEDBACK (OR RECURSIVE) FILTERS
1.11 SELF-ASSESSMENT TEST
1.12 CHAPTER SUMMARY
1.13 PROBLEMS
Chapter 2: Discrete signals and systems
2.1 CHAPTER PREVIEW
2.2 SIGNAL TYPES
2.3 THE REPRESENTATION OF DISCRETE SIGNALS
2.4 SELF-ASSESSMENT TEST
2.5 RECAP
2.6 THE z-TRANSFORM
2.7 z-TRANSFORM TABLES
2.8 SELF-ASSESSMENT TEST
2.9 THE TRANSFER FUNCTION FOR A DISCRETE SYSTEM
2.10 SELF-ASSESSMENT TEST
2.11 MATLAB AND SIGNALS AND SYSTEMS
2.12 RECAP
2.13 DIGITAL SIGNAL PROCESSORS AND THE z-DOMAIN
2.14 FIR FILTERS AND THE z-DOMAIN
2.15 IIR FILTERS AND THE z-DOMAIN
2.16 SELF-ASSESSMENT TEST
2.17 RECAP
2.18 CHAPTER SUMMARY
2.19 PROBLEMS
Chapter 3: The z-plane
3.1 CHAPTER PREVIEW
3.2 POLES, ZEROS AND THE s-PLANE
3.3 POLE–ZERO DIAGRAMS FOR CONTINUOUS SIGNALS
3.4 SELF-ASSESSMENT TEST
3.5 RECAP
3.6 FROM THE s-PLANE TO THE z-PLANE
3.7 STABILITY AND THE z-PLANE
3.8 DISCRETE SIGNALS AND THE z-PLANE
3.9 ZEROS
3.10 THE NYQUIST FREQUENCY
3.11 SELF-ASSESSMENT TEST
3.12 THE RELATIONSHIP BETWEEN THE LAPLACE AND z-TRANSFORM
3.13 RECAP
3.14 THE FREQUENCY RESPONSE OF CONTINUOUS SYSTEMS
3.15 SELF-ASSESSMENT TEST
3.16 THE FREQUENCY RESPONSE OF DISCRETE SYSTEMS
3.17 UNSTABLE SYSTEMS
3.18 SELF-ASSESSMENT TEST
3.19 RECAP
3.20 CHAPTER SUMMARY
3.21 PROBLEMS
Chapter 4: The design of IIR filters
4.1 CHAPTER PREVIEW
4.2 FILTER BASICS
4.3 FIR AND IIR FILTERS
4.4 THE DIRECT DESIGN OF IIR FILTERS
4.5 SELF-ASSESSMENT TEST
4.6 RECAP
4.7 THE DESIGN OF IIR FILTERS VIA ANALOGUE FILTERS
4.8 THE BILINEAR TRANSFORM
4.9 SELF-ASSESSMENT TEST
4.10 THE IMPULSE-INVARIANT METHOD
4.11 SELF-ASSESSMENT TEST
4.12 POLE–ZERO MAPPING
4.13 SELF-ASSESSMENT TEST
4.14 MATLAB AND s-TO-z TRANSFORMATIONS
4.15 CLASSIC ANALOGUE FILTERS
4.16 FREQUENCY TRANSFORMATION IN THE s-DOMAIN
4.17 FREQUENCY TRANSFORMATION IN THE z-DOMAIN
4.18 SELF-ASSESSMENT TEST
4.19 RECAP
4.20 PRACTICAL REALIZATION OF IIR FILTERS
4.21 CHAPTER SUMMARY
4.22 PROBLEMS
Chapter 5: The design of FIR filters
5.1 CHAPTER PREVIEW
5.2 INTRODUCTION
5.3 PHASE-LINEARITY AND FIR FILTERS
5.4 RUNNING AVERAGE FILTERS
5.5 THE FOURIER TRANSFORM AND THE INVERSE FOURIER TRANSFORM
5.6 THE DESIGN OF FIR FILTERS USING THE FOURIER TRANSFORM OR ‘WINDOWING’ METHOD
5.7 WINDOWING AND THE GIBBS PHENOMENON
5.8 HIGHPASS, BANDPASS AND BANDSTOP FILTERS
5.9 SELF-ASSESSMENT TEST
5.10 RECAP
5.11 THE DISCRETE FOURIER TRANSFORM AND ITS INVERSE
5.12 THE DESIGN OF FIR FILTERS USING THE ‘FREQUENCY SAMPLING’ METHOD
5.13 SELF-ASSESSMENT TEST
5.14 RECAP
5.15 THE FAST FOURIER TRANSFORM AND ITS INVERSE
5.16 MATLAB AND THE FFT
5.17 RECAP
5.18 A FINAL WORD OF WARNING
5.19 CHAPTER SUMMARY
5.20 PROBLEMS
Answers to self-assessment tests and problems
References and Bibliography
Appendix A: Some useful Laplace and z-transforms
Appendix B: Frequency transformations in the s- and z-domains
Index
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Appendix B: Frequency transformations in the s- and z-domains
Appendix A
Some useful Laplace and
z
-transforms
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