Sampling in Digital Signal Processing and Control

ISBN-13: 9781461275466 / Angielski / Miękka / 2011 / 544 str.

Arie Feuer; Graham Goodwin

Opis

Undoubtably one of the key factors influencing recent technology has been the advent of high speed computational tools. Virtually every advanced engi neering system we come in contact with these days depends upon some form of sampling and digital signal processing. Well known examples are digital tele phone systems, digital recording of audio signals and computer control. These developments have been matched by the appearance of a plethora of books which explain a variety of analysis, synthesis and design tools applica ble to sampled-data systems. The reader might therefore wonder what is distinc tive about the current book. Our observation of the existing literature is that the underlying continuous-time system is usually forgotten once the samples are tak en. The alternative point of view, adopted in this book, is to formulate the analy sis in such a way that the user is constantly reminded of the presence of the under lying continuous-time signals. We thus give emphasis to two aspects of sampled-data analysis: Firstly, we formulate the various algorithms so that the appropriate contin uous-time case is approached as the sampling rate increases. Secondly we place emphasis on the continuous-time output response rath er than simply focusing on the sampled response."

Spis treści

1 Fourier Analysis.- 1.1 Introduction.- 1.2 The Basic Transforms.- 1.2.1 Fourier Series.- 1.2.2 The Continuous-Time Fourier Transform.- 1.2.3 The Discrete-Time Fourier Transform (DTFT).- 1.2.4 The Discrete Fourier Transform (DFT).- 1.3 Properties of Continuous-Time Fourier Transforms.- 1.4 Properties of Discrete-Time Fourier Transforms.- 1.5 The ? — Impulse Stream.- 1.6 Inter-relating the Various Transforms.- 1.6.1 Fourier Series Revisited.- 1.6.2 The Discrete-Time Fourier Transform Revisited.- 1.6.3 The Discrete Fourier Transform Revisited.- 1.6.4 Summary.- 1.7 Special Topics.- 1.7.1 Sampling of Sequences.- 1.7.2 Irregular Sampling in Periodic Patterns.- 1.8 Further Reading and Discussion.- 1.9 Problems.- 2 Sampling and Reconstruction.- 2.1 Introduction.- 2.2 Sampled Data Sequences — A Representation of Continuous Signals.- 2.3 Continuous Signal Reconstruction from a Sampled Data Sequence.- 2.4 Shannon’ s Reconstruction Theorem.- 2.5 Practical Methods of Reconstruction.- 2.5.1 Zero-Order-Hold (ZOH).- 2.5.2 First-Order-Hold (FOH).- 2.6 Signal Reconstruction from Periodic Samples.- 2.7 Further Reading and Discussion.- 2.8 Problems.- 3 Analysis of Discrete-Time Systems.- 3.1 Introduction.- 3.2 Shift Operator Models.- 3.3 z-Transforms.- 3.4 The Delta Operator.- 3.5 Difference Equations in Delta Operator Form.- 3.6 Discrete Delta Transform.- 3.7 Use of Discrete Delta Transforms to Solve Difference Equations.- 3.8 The Discrete Transfer Function.- 3.9 Summary of Delta Transform Properties.- 3.10 Stability of Discrete Systems.- 3.11 Discrete Frequency Response.- 3.12 Frequency Domain Stability Criteria for Discrete-Time Systems.- 3.13 Digital Filter Implementation.- 3.14 Further Reading and Discussion.- 3.15 Problems.- 4 Discrete-Time Models of Continuous Deterministic Systems.- 4.1 Introduction.- 4.2 State-Space Development.- 4.3 Transform Development.- 4.4 Continuous-Time and Discrete-Time Poles and Zeros.- 4.4.1 Poles.- 4.4.2 Zeros.- 4.5 Numerical Issues.- 4.6 Frequency Domain Development.- 4.7 Further Reading and Discussion.- 4.8 Problems.- 5 Optimal Linear Estimation with Finite Impulse Response Filters.- 5.1 Introduction.- 5.2 Problem Description.- 5.3 Sampled Model.- 5.4 The Discrete Lattice Filter.- 5.5 Continuous-Time Lattice Structure.- 5.6 Relationships between the Discrete and Continuous Lattice Filters.- 5.7 Further Reading and Discussion.- 5.8 Problems.- 6 Optimal Linear Estimation with State-Space Filters.- 6.1 Introduction.- 6.2 Signal Model.- 6.3 The Sampling Process.- 6.4 Discrete Stochastic Model.- 6.5 The Discrete Kalman Filter.- 6.5.1 Model Simplification.- 6.5.2 The Optimal Filter.- 6.5.3 Relationship to Finite Impulse Response Filters.- 6.6 Continuous-Time State Estimation.- 6.6.1 Continuous-Time Data.- 6.6.2 Sampled Data.- 6.6.3 Relationships to Shannon Reconstruction Theorem.- 6.7 Further Reading and Discussion.- 6.8 Problems.- 7 Periodic and Multirate Filtering.- 7.1 Introduction.- 7.2 Models for Periodic Linear Systems.- 7.3 The Raising Procedure.- 7.4 Frequency Domain Analysis of Periodic Filters.- 7.5 Models for Sampled Periodic Stochastic Systems.- 7.6 Periodic Optimal Filtering.- 7.7 Further Reading and Discussion.- 7.8 Problems.- 8 Discrete-Time Control.- 8.1 Introduction.- 8.2 Closed-Loop Stability and Pole Assignment.- 8.3 Some Special Discrete-Time Control Laws.- 8.3.1 Deadbeat Control.- 8.3.2 Model Reference Control.- 8.3.3 Minimal Prototype Control.- 8.4 Sensitivity and Complementary Sensitivity Functions.- 8.5 All Stabilizing Control Laws.- 8.5.1 Open Loop Stable Plants.- 8.5.2 Open-Loop Unstable Plants.- 8.6 State Estimate Feedback.- 8.7 Rapprochement Between State Estimate Feedback and Stabilizing Controllers.- 8.7.1 Implicit Disturbance Modelling.- 8.7.2 Explicit Disturbance Modelling.- 8.8 Linear Quadratic Optimal Regulator.- 8.9 Duality Relationships.- 8.9.1 Filtering as a Control Problem.- 8.9.2 Associations.- 8.10 Further Reading and Discussion.- 8.11 Problems.- 9 Sampled Data Control.- 9.1 Introduction.- 9.2 Mixing Continuous and Discrete Transfer Functions.- 9.3 Sensitivity Considerations.- 9.4 Modified Discrete Transforms.- 9.5 Examples.- 9.5.1 Servo System with Minimal Prototype Controller.- 9.5.2 Servo System with Dead-Beat Control.- 9.5.3 Resonant System #1.- 9.5.4 Resonant System #2 with Anti-aliasing Filter.- 9.6 Observations and Comments from the Examples.- 9.7 The Class of All Stabilizing Sampled-Data Controllers.- 9.8 Linear Quadratic Design of Sampled-Data Controllers.- 9.9 Duality Relationships for Hybrid Optimal Controller.- 9.9.1 Review of Hybrid Optimal Controller.- 9.9.2 Review of Hybrid Optimal Filter.- 9.9.3 Duality.- 9.10 Further Reading and Discussion.- 9.11 Problems.- 10 Generalized Sample-Hold Functions.- 10.1 Introduction.- 10.2 Generalized Sample-Hold Function: A Time Domain Perspective.- 10.3 Other Applications of Generalized Sample-Hold Functions.- 10.4 Frequency Domain Analysis of GSHF.- 10.5 Sensitivity Considerations.- 10.6 Further Reading and Discussion.- 10.7 Problems.- 11 Periodic Control of Linear Time-Invariant Systems.- 11.1 Introduction.- 11.2 Periodic Control of Linear Time-Invariant Systems.- 11.3 Time Domain Analysis.- 11.4 Frequency Domain Analysis.- 11.5 Further Reading and Discussion.- 11.6 Problems.- 12 Multirate Control.- 12.1 Introduction.- 12.2 A Unifying Approach.- 12.3 Slow Output Sampling, Fast Input Sampling.- 12.4 Fast Output Sampling, Slow Input Sampling.- 12.5 Further Reading and Discussion.- 12.6 Problems.- 13 Optimal Control of Periodic Systems.- 13.1 Introduction.- 13.2 Control of Linear Periodic Systems.- 13.3 Control based on State Estimate Feedback.- 13.4 Further Reading and Discussion.- 13.5 Problems.