Introduction to Digital Filters

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Introduction to Digital Filters
Trevor J. Terrell
THE MACMILLAN PRESS LTD., 1980

Preface ix

1 Introduction 1
1.1 Background to Digital Filters 1
1.2 Sampled-data Signals 3
1.3 The Z-transform 6
1.4 Method of Determining Z-transforms from Laplace Transforms 21
1.5 The Inverse Z- transform 23
1.6 The Digital Filter Transfer Function 26
1.7 The Discrete Fourier Transform 32
1.8 The Fast Fourier Transform 34
1.9 Concluding Remarks 37

2 Design of Recursive Digital Filters 40
2.1 Introduction 40
2.2 Indirect Approach using Prototype Continuous Filter 41
2.3 Frequency Sampling Filters 68
2.4 Direct Approach using Squared Magnitude Function 77
2.5 Wave-shaping Filters 80

3 Design of Non-recursive Digital Filters 89
3.1 Introduction 89
3.2 Frequency-domain Design using Window Functions 90
3.3 Equiripple Approximation Method 95
3.4 An Analytical Technique for Designing FIR Filters 100
3.5 Time-domain Design of the Digital Transversal Filter 109

4 Quantisation Considerations in Digital Filter Implementation  112
4.1 Introduction 112
4.2 Binary Number Representations 113
4.3 Quantisation of the Digital Filter Input Signal 117
4.4 Realisation Structure Considerations 121
4.5 Umit Cycle Oscillations 139
4.6 Overflow Oscillations 143
4.7 Concluding Remarks 145

5 Practical Implementation of Digital Filters 148
5.1 Introduction 148
5.2 Implementation using Dedicated Hardware 148
5.3 Implementation using Digital Computers 164
5.4 Signals and Noise 186
5.5 Concluding Remarks 193

Appendixes to Chapter 5 194

Answers to Problems 212

Index 215

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