## Table of Contents

**1 Introduction**

1.1 Signals, Systems, and Signal Processing

1.2 Classification of Signals

1.3 The Concept of Frequency in Continuous-Time and Discrete-Time Signals

1.4 Analog-to-Digital and Digital-to-Analog Conversion

1.5 Summary and References

**2 Discrete-Time Signals And Systems**

2.1 Discrete-Time Signals

2.2 Discrete-Time Systems

2.3 Analysis of Discrete-Time Linear Time-Invariant systems

2.4 Discrete-Time Systems Described by Difference Equations

2.5 Implementation of Discrete-Time Systems

2.6 Correlation of Discrete-Time Signals

2.7 Summary and References

**3 The Z-Transform And Its Application To The Analysis Of Lti Systems**

3.1 The z-Transform

3.2 Properties of the z-Transform

3.3 Rational z-Transforms

3.4 Inversion of the z-Transform

3.5 Analysis of Linear Time Invariant Systems in the z-Domain

3.6 The One-sided z-Transform

3.7 Summary and References

**4 Frequency Analysis Of Signals And Systems**

4.1 Frequency Analysis of Continuous-Time Signals

4.2 Frequency Analysis of Discrete-Time Signals

4.3 Frequency-Domain and Time-Domain Signal Properties

4.4 Properties of the Fourier Transform for Discrete-Time Signals

4.5 Summary and References

**5 Frequency Domain Analysis Of Lti Systems**

5.1 Frequency-Domain Characteristics of Linear Time-Invariant Systems

5.2 Frequency Response of LTI Systems

5.3 Correlation Functions and Spectra at the Output of LTI Systems

5.4 Linear Time-Invariant Systems as Frequency-Selective Filters

5.5 Inverse Systems and Deconvolution

5.6 Summary and References

**6 Sampling And Reconstruction Of Signals**

6.1 Ideal Sampling and Reconstruction of Continuous-Time Signals

6.2 Discrete-Time Processing of Continuous-Time Signals

6.3 Analog-to-Digital and Digital-to-Analog Converters

6.4 Sampling and Reconstruction of Continuous-Time Bandpass Signals

6.5 Sampling of Discrete-Time Signals

6.6 Oversampling A/D and D/A Converters

6.7 Summary and References

**7 The Discrete Fourier Transform: Its Properties And Applications**

7.1 Frequency Domain Sampling:The Discrete Fourier Transform

7.2 Properties of the DFT

7.3 Linear Filtering Methods Based on the DFT

7.4 Frequency Analysis of Signals Using the DFT

7.5 The Discrete Cosine Transform

7.6 Summary and References

**8 Efficient Computaiton Of The Dft: Fast Fourier Transform Algorithms**

8.1 Efficient Computation of the DFT: FFT Algorithms

8.2 Applications of FFT Algorithms

8.3 A Linear Filtering Approach to Computation of the DFT

8.4 Quantization Effects in the Computation of the DFT

8.5 Summary and References

**9 Implementation Of Discrete-Time Systems**

9.1 Structures for the Realization of Discrete-Time Systems

9.2 Structures for FIR Systems

9.3 Structures for IIR Systems

9.4 Representation of Numbers

9.5 Quantization of Filter Coefficients

9.6 Round-Off Effects in Digital Filters

9.7 Summary and References

**10 Design Of Digital Filers**

10.1 General Considerations

10.2 Design of FIR Filters

10.3 Design of IIR Filters From Analog Filters

10.4 Frequency Transformations

10.5 Summary and References

**11 Multirate Digital Signal Processing**

11.1 Introduction

11.2 Decimation by a Factor D

11.3 Interpolation by a Factor I

11.4 Sampling Rate Conversion by a Rational Factor I/D

11.5 Implementation of Sampling Rate Conversion

11.6 Multistage Implementation of Sampling Rate Conversion

11.7 Sampling Rate Conversion of Bandpass Signals

11.8 Sampling Rate conversion by an Arbitrary Factor

11.9 Applications of Sampling Rate Conversion

11.10 Digital Filter Banks

11.11 Two-Channel Quadrature Mirror Filter Bank

11.12 M-Channel QMF Bank

11.13 Summary and References

**12 Linear Prediction And Optimum Linear Filters**

12.1 Random Signals, Correlation Functions and Power Spectra

12.2 Innovations Representation of a Stationary Random Process

12.3 Forward and Backward Linear Prediction

12.4 Solution of the Normal Equations

12.5 Properties of the Linear Prediction-Error Filters

12.6 AR Lattice and ARMA Lattice-Ladder Filters

12.7 Wiener Filters for Filtering and Prediction

12.8 Summary and References

**13 Adaptive Filters**

13.1 Applications of Adaptive Filters

13.2 Adaptive Direct-Form FIR Filters-The LMS Algorithm

13.3 Adaptive Direct-Form FIR Filters-RLS Algorithms

13.4 Adaptive Lattice-Ladder Filters

13.5 Summary and References

**14 Power Spectrum Estimation**

14.1 Estimation of Spectra from Finite-Duration Observations of Signals

14.2 Nonparametric Methods for Power Spectrum Estimation

14.3 Parametric Methods for Power Spectrum Estimation

14.4 Filter Bank Methods

14.5 Eigenanalysis Algorithms for Spectrum Estimation

14.6 Summary and References

**Appendices**

Appendix A Random Number Generators

Appendix B Tables of Transition Coefficients for the Design of Linear-Phase Filters

References and Bibliography

Index

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