Preface
Introduction
1 Discrete-time signals and 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 Impulse response and convolution sums
1.3.5 Stability
1.4 Difference equations and time-domain response
1.4.1 Recursive x no recursive systems
1.5 Song difference equations
1.5.1 Computing impulse responses
1.6 Sampling of continuous-time signals
1.6.1 Basic principles
1.6.2 Sampling theorem
1.7 Random signals
1.7.1 Random variable
1.7.2 Random processes
1.7.3 Filtering a random signal
1.8 Do-it-yourself: discrete-time signals and systems
1.9 Discrete-time signals and systems with MA lab
1.10 Summary
1.11 Exercises
2 The z and Fourier transforms
2.1 Introduction
2.2 Definition of the z transforms
2.3 Inverse z transform
2.3.1 Computation based on residue theorem
2.3.2 Computation based on partial-fraction expansions
2.3.4 Computation based on series expansion
2.4 Properties of the z transom
2.4.1 Linearity
2.4.2 Time reversal
2.4.3 Time-stuff 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 Parsifal''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 Time-shift theorem
2.9.4 Multiplication by a complex exponential frequency shift
modulation
2.9.5 Complex differentiation
2.9.6 Complex conjugation
2.9.7 Real and imaginary sequences
2.9.8 Symmetric and ant symmetric sequences
2.9.9 Convolution theorem
2.9.10 Product of two sequences
2.9.11 Parsifal''s theorem
2.10 Fourier transform for periodic sequences
2.11 Random signals in the transform domain
2.11.1 Powerspectraldensity
2.11.2 White noise
2.12 Do it-yourself: the z and Fourier transforms
2.13 The z and Fourier transforms with MATLAB
2.14 Summary
2.15 Exercises
3 Discrete transforms
3.1 Introduction
3.2 Discrete Fourier transform
3.3 Properties of the DFT
……
4 Digital Filters
5 Fir Filter Approximations
6 IIR Filter Approximations
7 Spectral Estimation
8 Multirate Systems
9 Filter Banks
10 Wavelet Transforms
11 Finite Precision Digital Signal Processing
12 Efficient Fir Structures
13 Efficient IIR Structures
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