Chapter 1 Discrete-Time Systems 1.1 Introduction 1.2 Discrete-Time Signals 1.3 Discrete-Time Systems 1.3.1 Linearity 1.3.2 Time Invariance 1.3.3 Causality 1.3.4 Stability 1.4 Difference Equations and Time-Domain Response 1.5 Sampling of Continuous-Time Signals 1.5.1 Basic Principles 1.5.2 Sampling Theorem 1.6 Discrete-Time Signals and Systems with MATLAB 1.7 Summary Exercises MATLAB Exercises Chapter 2 The z and Fourier Transforms 2.1 Introduction 2.2 Definition of the z Transform 2.3 Inverse z Transform 2.3.1 Computation Based on Residue Theorem 2.3.2 Computation Based on Partial-Fraction Expansions 2.3.3 Computation Based on Polynomial Division 2.3.4 Computation Based on Series Expansion 2.4 Properties of the z Transform 2.4.1 Linearity 2.4.2 Time-Reversal 2.4.3 Time-Shift Theorem 2.4.4 Multiplication by An Exponential 2.4.5 Complex Differentiation 2.4.6 Complex Conjugation 2.4.7 Real and Imaginary Sequences 2.4.8 Initial Value Theorem 2.4.9 Convolution Theorem 2.4.10 Product of Two Sequences 2.4.11 Parseval』s Theorem 2.4.12 Table of Basic z Transforms 2.5 Transfer Functions 2.6 Stability in the z Domain 2.7 Frequency Response 2.8 Fourier Transform 2.9 Properties of the Fourier Transform 2.9.1 Linearity 2.9.2 Time-Reversal 2.9.3 Symmetric and Antisymmetric Sequences 2.9.4 Convolution Theorem 2.9.5 Product of Two Sequences 2.9.6 Parseval』s Theorem 2.10 Transfer Functions with MATLAB 2.11 Summary
Exercises Chapter 3 Discrete Transforms 3.1 Introduction 3.2 Discrete Fourier Transform 3.3 Properties of the DFT 3.3.1 Linearity 3.3.2 Time-Reversal 3.3.3 Time-Shift Theorem 3.3.4 Circular Frequency-Shift Theorem (Modulation Theorem) 3.3.5 Circular Convolution in Time 3.3.6 Correlation 3.3.7 Real and Imaginary Sequences 3.3.8 Symmetric and Antisymmetric Sequences 3.3.9 Parseval』s Theorem 3.3.10 Relationship between the DFT and the z Transform 3.4 Digital Filtering Using the DFT 3.4.1 Linear and Circular Convolutions 3.4.2 Overlap-and-Add Method 3.4.3 Overlap-and-Save Method 3.5 Fast Fourier Transform 3.6 Other Discrete Transforms 3.6.1 Discrete Cosine Transform 3.6.2 Discrete Hartley Transform 3.6.3 Hadamard Transform 3.6.4 Other Important Transforms 3.7 Signal Representations 3.8 Discrete Transforms with MATLAB 3.9 Summary Exercises Chapter 4 The Fast Fourier Transform 4.1 Relationship of the FFT to the DFT 4.2 Hints on Using FFTs in Practice 4.2.1 Sample Fast Enough and Long Enough 4.2.2 Manipulating the Time Date Prior to Transformation 4.2.3 Enhancing FFT Results 4.2.4 Interpreting FFT Results 4.3 Derivation of the Radix-2 FFT Algorithm 4.4 FFT Input/Output Data Index Bit Reversal 4.5 Radix-2 FFT Butterfly Structures 4.6 Alternate Single-Butterfly Structures 4.7 Fast Fourier Transform with MATLAB 4.8 Summary Exercises MATLAB Exercises Chapter 5 Digital Filter Structures 5.1 Block Diagram Representation 5.1.1 Basic Building Blocks 5.1.2 Analysis of Block Diagrams 5.1.3 The Delay-Free Loop Problem 5.1.4 Canonic and Non-Canonic Structures
5.2 Equivalent Structures 5.3 Basic FIR Digital Filter Structures 5.3.1 Direct-Form Structures 5.3.2 Cascade-Form Structures 5.3.3 Polyphase Realization 5.3.4 Linear-Phase FIR Structures 5.3.5 Tapped Delay Line 5.4 Basic IIR Digital Filter Structures 5.4.1 Direct-Form Structures 5.4.2 Cascade Realizations 5.4.3 Parallel Realizations 5.5 Realization of Basic Structures Using MATLAB 5.5.1 Cascade Realization 5.5.2 Parallel Realization 5.6 Allpass Filters 5.6.1 Realization Based on the Multiplier Extraction Approach 5.6.2 Realization Based on the Two-Pair Extraction Approach 5.7 IIR Tapped Cascaded Lattice Structures 5.7.1 Realization of an All-Pole IIR Transfer Function 5.7.2 Gray-Markel Method 5.7.3 Realization Using MATLAB 5.8 FIR Cascaded Lattice Structures 5.8.1 Realization of a Pair of Arbitrary FIR Transfer Functions 5.8.2 Realization of a Pair of Mirror-Image FIR Transfer Functions 5.8.3 Realization of a Pair of Power-Complementary FIR Transfer Functions 5.8.4 Realization of a single FIR Transfer Function 5.8.5 Realization Using MATLAB 5.9 Summary Exercises MATLAB Exercises Chapter 6 IIR Digital Filter Design 6.1 Preliminary Considerations 6.1.1 Digital Filter Specifications 6.1.2 Selection of the Filter Type 6.1.3 Basic Approach to IIR Digital Filter Design 6.1.4 IIR Digital Filter Order Estimation 6.1.5 Scaling the Digital Transfer Function 6.2 Bilinear Transformation Method of IIR Filter Design 6.2.1 The Bilinear Transformation 6.2.2 Design of Low-Order Digital Filters 6.3 Design of Lowpass IIR Digital Filters 6.4 Design of Highpass, Bandpass, and Bandstop IIR Digital Filters 6.5 Spectral Transformation of IIR Filters 6.5.1 Lowpass-to-Lowpass Transformation 6.5.2 Other Transformations 6.5.3 Spectral Transformation Using MATLAB 6.6 IIR Digital Filter Design Using MATLAB 6.7 Summary Exercises MATLAB Exercises
Chapter 7 FIR Digital Filter Design 7.1 Preliminary Considerations 7.1.1 Basic Approaches to FIR Digital Filter Design 7.1.2 Estimation of the Filter Order 7.2 FIR Filter Design Based on Windowed Fourier Series 7.2.1 Least Integral-Squared Error Design of FIR Filters 7.2.2 Impulse Response Of Ideal Filters 7.2.3 Gibbs Phenomenon 7.2.4 Fixed Window Function 7.2.5 Adjustable Window Functions 7.2.6 Impulse Responses of FIR Filters with a Smooth Transition 7.3 Computer-Aided Design of Equiripple Linear-Phase FIR Filters 7.3.1 The Parks-McClellan Algorithm 7.3.2 The Shpak-Antoniou Algorithm 7.4 Design of Minimum-Phase FIR Filters 7.5 FIR Digital Filter Design Using MATLAB 7.5.1 FIR Digital Filter Order Estimation Using MATLAB 7.5.2 Equiripple Linear-Phase FIR Filter Design Using MATLAB 7.5.3 Minimum-Phase FIR Filter Design Using MATLAB 7.5.4 Window-Based FIR Filter esign Using MATLAB 7.6 Summary Exercises MATLAB Exercises Bibliography
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