Discrete-time Signal Processing: An Algebraic Approach

ISBN-13: 9781852331610 / Angielski / Miękka / 1999 / 421 str.

Darrell Williamson

Opis

The topics of control engineering and signal processing continue to flourish and develop. In common with general scientific investigation, new ideas, concepts and interpretations emerge quite spontaneously and these are then discussed, used, discarded or subsumed into the prevailing subject paradigm. Sometimes these innovative concepts coalesce into a new sub-discipline within the broad subject tapestry ofcontrol and signal processing. This preliminary battle between old and new usually takes place at conferences, through the internet and in the journals of the discipline. After a little more maturity has been acquired by the new concepts then archival publication as a scientific or engineering monograph may occur. The applications ofsignal processing techniques have grown and grown. They now cover the wide range from the statistical properties of signals and data through to the hardware problems of communications in all its diverse aspects. Supporting this range ofapplications is a body of theory, analysis and techniques which is equally broad. Darrell Williamson has faced the difficult task of organising this material by adopting an algebraic approach. This uses general mathematical and systems ideas and results to form a firm foundation for the discrete signal processing paradigm. Although this may require some extra concentration and involvement by the student or researcher, the rewards are a clarity of presentation and deeper insight into the power of individual results. An additional benefit is that the algebraic language used is the natural language of computing tools like MATLAB and its simulation facility, SIMULINK.

Spis treści

1. Introduction.- 1.1 Digital and Analog Signals.- 1.2 Digital-to-Analog Conversion.- 1.3 Analog-to-Digital Conversion.- 1.4 Signal Processing.- Summary.- Exercises.- 2. Digital Signals.- 2.1 First Order.- 2.1.1 Zero Input and Forced Response.- 2.1.2 Steady State and Transient Response.- 2.2 Second Order.- 2.2.1 Zero Input Response.- 2.2.2 Unit Impulse Response.- 2.3 High Order.- 2.3.1 Zero Input Response.- 2.3.2 Stability Test.- 2.4 Linear Convolution.- 2.4.1 Forced Response.- 2.4.2 Steady State Sinusoidal Response.- 2.5 State Space Representation.- 2.5.1 Second Order.- 2.5.2 High Order.- 2.5.3 Steady State Sinusoidal Response.- Summary.- Exercises.- 3. Digital Filters.- 3.1 Overview.- 3.2 Design of FIR Filters.- 3.2.1 Linear Phase.- 3.2.2 Windowing.- 3.3 Design of IIR Filters.- 3.3.1 All Pass Filter.- 3.3.2 Analog Filters.- 3.3.3 Analog State Space Representation.- 3.3.4 Analog to Digital Transformation.- 3.3.5 Digital to Digital Transformation.- Summary.- Exercises.- 4. Signal Processing.- 4.1 Fundamental Properties.- 4.1.1 Signal Norm.- 4.1.2 Signal Inner Product.- 4.1.3 Orthogonal Signals.- 4.1.4 Signal Bounds.- 4.2 Discrete Fourier Transform.- 4.2.1 Periodic Signal.- 4.2.2 Finite Length Signal.- 4.2.3 Properties of the DFT.- 4.2.4 Fast Fourier Transform.- 4.2.5 Linear Convolution via FFT.- 4.3 Least Squares Estimation.- 4.3.1 Linear Phase FIR Filter Design.- 4.3.2 Input-Output Signal Model.- 4.3.3 State Space Signal Model.- 4.3.4 Recursive Estimation.- 4.3.5 Applications of Recursive Estimation.- Summary.- Exercises.- 5. Finite Wordlength IIR Filter Implementation.- 5.1 Arithmetic Format.- 5.1.1 Fixed Point.- 5.1.2 Floating Point.- 5.2 First Order FWL Filter.- 5.2.1 Quantization Errors.- 5.2.2 Scaling.- 5.3 Second Order FWL Filter.- 5.3.1 Quantization Errors.- 5.3.2 Scaling.- 5.4 State Space FWL Filter.- 5.4.1 Quantization Errors.- 5.4.2 Scaling.- 5.5 Filter Structures.- 5.5.1 Error Performance Measure.- 5.5.2 Low Complexity Structures.- 5.5.3 Delay Replaced Structures.- 5.5.4 Optimal Structures.- Summary.- Exercises.