Contents

Foreword

Preface

Acknowledgements

1 Processing of Signals

1.1 Organisation of the Book

1.2 Classification of Signals

1.2.1 Spectral Domain

1.2.2 Random Signals

1.2.3 Periodic Signals

1.3 Transformations

1.3.1 Laplace and Fourier Transforms

1.3.2 The z-Transform and the Discrete Fourier Transform

1.3.3 An Interesting Note

1.4 Signal Characterisation

1.4.1 Non-parametric Spectrum or Fourier Spectrum

1.4.2 Parametric Representation

1.5 Converting Analogue Signals to Digital

1.5.1 Windowing

1.5.2 Sampling

1.5.3 Quantisation

1.5.4 Noise Power

1.6 Signal Seen by the Computing Engine

1.6.1 Mitigating the Problems

1.6.2 Anatomy of a Converter

1.6.3 The Need for Normalised Frequency

1.6.4 Care before Sampling

1.7 It Is Only Numbers

1.7.1 Numerical Methods

1.8 Summary

References

2 Revisiting the Basics

2.1 Linearity

2.1.1 Linear Systems

2.1.2 Sinusoidal Inputs

2.1.3 Stability

2.1.4 Shift Invariance

2.1.5 Impulse Response

2.1.6 Decomposing h_k

2.2 Linear System Representation

2.2.1 Continuous to Discrete

2.2.2 Nomenclature

2.2.3 Difference Equations

2.2.4 Transfer Function

2.2.5 Pole–Zero Representation

2.2.6 Continuous to Discrete Domain

2.2.7 State Space Representation

2.2.8 Solution of Linear Difference Equations

2.3 Random Variables

2.3.1 Functions of a Random Variable

2.3.2 Reliability of Systems

2.4 Noise

2.4.1 Noise Generation

2.4.2 Fourier Transform and pdf of Noise

2.5 Propagation of Noise in Linear Systems

2.5.1 Linear System Driven by Arbitrary Noise

2.6 Multivariate Functions

2.6.1 Vectors of More Than Two Dimensions

2.6.2 Functions of Several Variables

2.6.3 System of Equations

2.7 Number Systems

2.7.1 Representation of Numbers

2.7.2 Fixed-Point Numbers

2.7.3 Floating-Point Numbers

2.8 Summary

References

3 Digital Filters

3.1 How to Specify a Filter

3.2 Moving-Average Filters

3.2.1 Area under a Curve

3.2.2 Mean of a Given Sequence

3.2.3 Mean over a Fixed Number of Samples

3.2.4 Linear Phase Filters

3.2.5 MA Filter with Complex Coefficients

3.3 Infinite Sequence Generation

3.3.1 Digital Counter

3.3.2 Noise Sequence

3.3.3 Numerically Controlled Oscillator

3.4 Unity-Gain Narrowband Filter

3.5 All-Pass Filter

3.5.1 Interpolation of Data Using an APF

3.5.2 Delay Estimation Using an APF

3.6 Notch Filter

3.6.1 Overview

3.7 Other Autoregressive Filters

3.8 Adaptive Filters

3.8.1 Varying r

3.8.2 Varying p

3.8.3 Criteria

3.8.4 Adaptation

3.9 Demodulating via Adaptive Filters

3.9.1 Demodulation Method

3.9.2 Step Size μ

3.9.3 Performance

3.10 Phase Shift via Adaptive Filter

3.11 Inverse Problems

3.11.1 Model Order Problem

3.11.2 Estimating Filter Coefficients

3.11.3 Target Tracking as an Inverse Problem

3.12 Kalman Filter

3.12.1 Estimating the Rate

3.12.2 Fitting a Sine Curve

3.12.3 Sampling in Space

3.13 Summary

References

4 Fourier Transform and Signal Spectrum

4.1 Heterodyne Spectrum Analyser

4.1.1 Spectrum Analyser

4.2 Discrete Fourier Transform

4.3 Decimating the Given Sequence

4.3.1 Sliding DFT

4.4 Fast Fourier Transform

4.4.1 Windowing Effect

4.4.2 Frequency Resolution

4.4.3 Decimation in Time

4.4.4 Decimation in Frequency

4.4.5 Computing Effort Estimate

4.5 Fourier Series Coefficients

4.5.1 Fourier Coefficients

4.6 Convolution by DFT

4.6.1 Circular Convolution

4.7 DFT in Real Time

4.7.1 Vehicle Classification

4.7.2 Instrument Classification

4.8 Frequency Estimation via DFT

4.8.1 Problem Definition

4.8.2 DFT Solution

4.9 Parametric Spectrum in RF Systems

4.9.1 Test Data Generation

4.9.2 Estimating the Parameter Vector

4.10 Summary

References

5 Realisation of Digital Filters

5.1 Evolution

5.2 Development Process

5.3 Analogue-to-Digital Converters

5.3.1 Successive Approximation Method

5.3.2 Flash Converters

5.3.3 Sigma–Delta Converters

5.3.4 Synchro-to-Digital Converters

5.4 Second-Order BPF

5.4.1 Fixed-Point Implementation

5.5 Pipelining Filters

5.5.1 Modelling Hardware Multipliers and Adders

5.5.2 Pipelining FIR Filters

5.5.3 Pipelining IIR Filters

5.5.4 Stability Issues

5.6 Real-Time Applications

5.6.1 Comparison of DSP Processors

5.7 Frequency Estimator on the DSP5630X

5.7.1 Modified Response Error Method

5.7.2 Algorithm to Code

5.8 FPGA Implementation of a Kalman Filter

5.8.1 Fixed-Point Implementation

5.9 Summary

References

6 Case Studies

6.1 Difference Equation to Program

6.2 Estimating Direction of Arrival

6.3 Electronic Rotating Elements

6.3.1 Problem Formulation

6.3.2 Finding the DoA

6.3.3 Straight-Line Fit

6.4 Summary

References

Appendix: MATLAB and C Programs

A.1 Chapter 1 MATLAB Programs

A.1.1 Program f1_1234

A.1.2 Program f1_56

A.1.3 Program f1_78

A.1.4 Program f11_901

A.1.5 Program f11_23458

A.2 Chapter 2 MATLAB Programs

A.2.1 Program f2_345

A.2.2 Program f2_7

A.2.3 Program f2_7b

A.2.4 Program f2_8a

A.2.5 Program f2_89

A.2.6 Program f21_0123

A.2.7 Program f21_67

A.3 Chapter 3 MATLAB Programs

A.3.1 Program f3_1

A.3.2 Program f3_1a

A.3.3 Program f3_2

A.3.4 Program f3_3

A.3.5 Program f3_45

A.3.6 Program f3_6

A.3.7 Program f31_4

A.3.8 Program f31_5

A.3.9 Program f31_6a

A.3.10 Program f31_78

A.3.11 Program f3_789

A.3.12 Program f31_90

A.3.13 Program f31_9a

A.3.14 Program f3_6_1a

A.3.15 Program f3_65

A.3.16 Program f3_6_9

A.3.17 Program f3_61_01

A.3.18 Program f3_61_4

A.3.19 Program f32_6a

A.4 Chapter 4 MATLAB Programs

A.4.1 Program f4_4

A.4.2 Program f4_56

A.4.3 Program f4_62_0

A.4.4 Program f4_6_2

A.4.5 Program f4_61_5b

A.5 Chapter 5 Programs

A.5.1 MATLAB Program f5_7a

A.5.2 MATLAB Program f51_1

A.5.3 MATLAB Program f51_2

A.5.4 MATLAB Program f51_3

A.5.5 C Program f51_2

A.6 Chapter 6 MATLAB Programs

A.6.1 Program f6_9b

A.6.2 Program f6_3

A.7 Library of Subroutines

A.7.1 Program Expand

A.7.2 Program freq

A.7.3 Program freqt

A.7.4 Program rbn_sig

A.7.5 Program p2f1

A7.6 Program pulse

A7.7 Program forier

A.7.8 Program spk

A.7.9 Program pdf_y

A.8 Some Useful Programs

A.8.1 Program f2_grad

A.8.2 Program f2_lemma

A.8.3 Program f5_pipe

A.8.4 Program f3_rate

Index