Discrete-Time Signal Processing : An Algebraic Approach

by Williamson, Darrell

• ISBN13: 9781852331610
• ISBN10: 1852331615
• Format: Paperback
• Copyright: 1999-09-01
• Publisher: Springer Verlag

Summary

This text is intended to be used by postgraduate and advanced undergraduate students in the study of discrete-time integrals. It focuses on an algebraic approach to the analysis and design of discrete-time signal processing algorithms which renders the Laplace and z-transforms redundant for this purpose. While the material on difference equations is developed slowly, from an elementary base, it is assumed that the reader has a working knowledge of complex numbers and has completed a first course in vector and matrix analysis. Various subjects and problems are discussed including: - The solution of both difference and state space equations - Provides an alternative approach to the use of Laplace and z-transformations - Linear-algebraic ideas for the analysis and design of linear signals - The Design of recursive (IIR) and nonrecursive (FIR) digital filters - The design of classical Butterworth, Chebyshev and Elliptical analog filters and the transformation of analog filters - The Discrete Fourier Transform and its implementation through the Fast Fourier Transform - Applications of least-squares analysis to the design of linear phase FIR filters, convolution (FIR and IIR) signal models, and state space signal models - Design of digital filters via discrete approximation of analog filters, digital transformation of analog filter, and digital transformation of digital filter - Finite wordlength (FWL) implementation of IIR digital filters including the basic properties of both fixed and floating point arithmetic representations, implication of arithmetic quantizations and filter structure on accuracy and speed of real-time implementation - Written with clarity and containing the latest, detailed results based on comprehensive research, this book is an important textbook for all students interested in discrete-time signals - The text supports the use of algebra-based software packages, such as MATLAB .

Table of Contents

Introduction	1	(34)
Digital and Analog Signals	2	(7)
Digital-to-Analog Conversion	9	(3)
Analog-to-Digital Conversion	12	(4)
Signal Processing	16	(19)
Summary	29	(2)
Exercises	31	(4)
Digital Signals	35	(88)
First Order	35	(18)
Zero Input and Forced Response	41	(9)
Steady State and Transient Response	50	(3)
Second Order	53	(20)
Zero Input Response	59	(10)
Unit Impulse Response	69	(4)
High Order	73	(8)
Zero Input Response	73	(6)
Stability Test	79	(2)
Linear Convolution	81	(11)
Forced Response	82	(3)
Steady State Sinusoidal Response	85	(7)
State Space Representation	92	(31)
Second Order	92	(12)
High Order	104	(6)
Steady State Sinusoidal Response	110	(1)
Summary	111	(3)
Exercises	114	(9)
Digital Filters	123	(90)
Overview	123	(13)
Design of FIR Filters	136	(10)
Linear Phase	136	(5)
Windowing	141	(5)
Design of IIR Filters	146	(67)
All Pass Filter	147	(4)
Analog Filters	151	(14)
Analog State Space Representation	165	(9)
Analog to Digital Transformation	174	(12)
Digital to Digital Transformation	186	(9)
Summary	195	(2)
Exercises	197	(16)
Signal Processing	213	(114)
Fundamental Properties	213	(38)
Signal Norm	219	(5)
Signal Inner Product	224	(6)
Orthogonal Signals	230	(11)
Signal Bounds	241	(10)
Discrete Fourier Transform	251	(38)
Periodic Signal	251	(10)
Finite Length Signal	261	(2)
Properties of the DFT	263	(5)
Fast Fourier Transform	268	(9)
Linear Convolution via FFT	277	(12)
Least Squares Estimation	289	(38)
Linear Phase FIR Filter Design	292	(4)
Input-Output Signal Model	296	(5)
State Space Signal Model	301	(6)
Recursive Estimation	307	(3)
Applications of Recursive Estimation	310	(4)
Summary	314	(1)
Exercises	315	(12)
Finite Wordlength IIR Filter Implementation	327	(92)
Arithmetic Format	327	(13)
Fixed Point	328	(7)
Floating Point	335	(5)
First Order FWL Filter	340	(16)
Quantization Errors	345	(6)
Scaling	351	(5)
Second Order FWL Filter	356	(8)
Quantization Errors	356	(5)
Scaling	361	(3)
State Space FWL Filter	364	(20)
Quantization Errors	369	(9)
Scaling	378	(6)
Filter Structures	384	(35)
Error Performance Measure	384	(3)
Low Complexity Structures	387	(13)
Delay Replaced Structures	400	(2)
Optimal Structures	402	(6)
Summary	408	(1)
Exercises	409	(10)
Index	419