# Digital Signal Processing and Statistical Classification

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Description

This is the first book to introduce and integrate the topics of digital signal processing (DSP) and statistical classification together, and the only volume to introduce state-of-the-art transforms, including DFT, FFT, DCT, DST, DHT, DHLT, DFHT, DTWT, DWT, DHAT, PCT, CCT, CDT, and ODT together for DSP and digital communication applications. You get step-by-step guidance in: discrete-time random processes; discrete-time domain signal processing and frequency domain signal analysis; discrete-time transforms; digital filter design and adaptive filtering; multirate digital signal processing; and statistical signal classification. The text also helps you overcome problems associated with multirate A/D and D/A converters. Extensively referenced with over 1,065 equations, 142 illustrations, and numerous examples, the book furnishes an up-to-date, comprehensive, and coherent treatment of the fundamentals of this cutting-edge technology, based on the academic and industry experience of the authors. An excellent technical reference and research tool for both practicing engineers and graduate students in electrical, computer, and other engineering disciplines, this book offers assistance in applying DSP knowledge and statistical classification in real world applications. This authoritative volume includes critical concepts never before covered in this detail.

This is the first book to introduce and integrate the topics of digital signal processing (DSP) and statistical classification together, and the only volume to introduce state-of-the-art transforms, including DFT, FFT, DCT, DST, DHT, DHLT, DFHT, DTWT, DWT, DHAT, PCT, CCT, CDT, and ODT together for DSP and digital communication applications. You get step-by-step guidance in: discrete-time random processes; discrete-time domain signal processing and frequency domain signal analysis; discrete-time transforms; digital filter design and adaptive filtering; multirate digital signal processing; and statistical signal classification. The text also helps you overcome problems associated with multirate A/D and D/A converters. Extensively referenced with over 1,065 equations, 142 illustrations, and numerous examples, the book furnishes an up-to-date, comprehensive, and coherent treatment of the fundamentals of this cutting-edge technology, based on the academic and industry experience of the authors. An excellent technical reference and research tool for both practicing engineers and graduate students in electrical, computer, and other engineering disciplines, this book offers assistance in applying DSP knowledge and statistical classification in real world applications. This authoritative volume includes critical concepts never before covered in this detail.

Table Of Contents

About the Authors; Preface; Introduction--Data Acquisition System. DSP Algorithms. Statistical Signal Classification. Scope of This Book. References.; Discrete-Time Signal Processing-Introduction. Discrete-Time Signals. Basic Operations of Discrete-Time Signals. Discrete-Time Systems. Linear Time-Invariant Discrete-Time Systems. The z-Transform. The Inverse z-Transform. Frequency Domain of Discrete-Time Signals and Systems. The Relationship of Allpass and Minimum-Phase Systems. Summary. References.; Discrete-Time Random Processes--Introduction. Probability and Random Variables. Distribution and Density Functions. Stochastic Processes. Summary. References.; Discrete-Time Transforms--Introduction. The Discrete Fourier Transform. The Fast Fourier Transform. The Discrete Cosine Transform. The Discrete Sine Transforms. The Discrete Hartley Transform. The Discrete Hilbert Transform. The Discrete Fractional Hilbert Transform. The Discrete-Time Wavelet Transform. The Discrete Walsh Transform. The Discrete Hadamard Transform. Summary. References.; Digital Filtering-Introduction. Filter Specifications. FIR Linear Phase. FIR Filter Design. IIR Filter Design. Implementation of Filter Structures. Summary. References.; Adaptive Filters--Introduction. Wiener Filter Theory. Discrete-Time Kalman Filter. The LMS Adaptive Filters. Recursive Least Squares Algorithms. Summary. References.; Discrete-Time Multirate Signal Processing-Introduction. Decimation and Interpolation System. Efficient Polyphase Architecture for Implementing Multirate Signal Processing System. Efficient Design Techniques of Multiband Filters. Multistage Design of Multirate Signal Processing. Multirate Filter Banks. The Uniform DFT Filter Bank. Multirate Adaptive Filter Banks. Summary. References.; Multirate Data Converters-Introduction. Analog-To-Digital Converter. Digital-To-Analog Converter. Multirate A/D Converter. Multirate D/A Converter. Oversampling A/D Converters. Sigma-Delta A/D Converter. Hybrid QMF Bank A/D and D/A Converter. Summary. References.; Statistical Signal Classification-Introduction. Statistical Pattern Representation. Feature Extraction Theory. Unsupervised Learning and Cluster Analysis. Signal Classification. Estimated Probability of Misclassification. Summary. References.; Transform-Based Statistical Signal Classification-Introduction. System Architectures of Transform-Based Statistical Signal Classification. Generalized Principal Components Transform. Canonical Correlation Transform. Canonical Discrimination Transform. Optimal Discriminant Transform.; Generalized Optimal Declustering Transform. Transform-Based Statistical Signal Classifiers. Application and Performance Evaluations. Summary. References.; Appendix A--Matrix Algebra of Linear Transformation. Vectors. Matrices. The Data Matrix. Orthogonal Matrices and the Trace. Matrix Differentiation. Eigenvalues and Eigenvectors. Theorem of Spectral Decomposition. Theorem of Singular Value Decomposition. Quadratic Forms. Maximization and Minimization Theorem. References.; List of Figures.; Index.;

About the Authors; Preface; Introduction--Data Acquisition System. DSP Algorithms. Statistical Signal Classification. Scope of This Book. References.; Discrete-Time Signal Processing-Introduction. Discrete-Time Signals. Basic Operations of Discrete-Time Signals. Discrete-Time Systems. Linear Time-Invariant Discrete-Time Systems. The z-Transform. The Inverse z-Transform. Frequency Domain of Discrete-Time Signals and Systems. The Relationship of Allpass and Minimum-Phase Systems. Summary. References.; Discrete-Time Random Processes--Introduction. Probability and Random Variables. Distribution and Density Functions. Stochastic Processes. Summary. References.; Discrete-Time Transforms--Introduction. The Discrete Fourier Transform. The Fast Fourier Transform. The Discrete Cosine Transform. The Discrete Sine Transforms. The Discrete Hartley Transform. The Discrete Hilbert Transform. The Discrete Fractional Hilbert Transform. The Discrete-Time Wavelet Transform. The Discrete Walsh Transform. The Discrete Hadamard Transform. Summary. References.; Digital Filtering-Introduction. Filter Specifications. FIR Linear Phase. FIR Filter Design. IIR Filter Design. Implementation of Filter Structures. Summary. References.; Adaptive Filters--Introduction. Wiener Filter Theory. Discrete-Time Kalman Filter. The LMS Adaptive Filters. Recursive Least Squares Algorithms. Summary. References.; Discrete-Time Multirate Signal Processing-Introduction. Decimation and Interpolation System. Efficient Polyphase Architecture for Implementing Multirate Signal Processing System. Efficient Design Techniques of Multiband Filters. Multistage Design of Multirate Signal Processing. Multirate Filter Banks. The Uniform DFT Filter Bank. Multirate Adaptive Filter Banks. Summary. References.; Multirate Data Converters-Introduction. Analog-To-Digital Converter. Digital-To-Analog Converter. Multirate A/D Converter. Multirate D/A Converter. Oversampling A/D Converters. Sigma-Delta A/D Converter. Hybrid QMF Bank A/D and D/A Converter. Summary. References.; Statistical Signal Classification-Introduction. Statistical Pattern Representation. Feature Extraction Theory. Unsupervised Learning and Cluster Analysis. Signal Classification. Estimated Probability of Misclassification. Summary. References.; Transform-Based Statistical Signal Classification-Introduction. System Architectures of Transform-Based Statistical Signal Classification. Generalized Principal Components Transform. Canonical Correlation Transform. Canonical Discrimination Transform. Optimal Discriminant Transform.; Generalized Optimal Declustering Transform. Transform-Based Statistical Signal Classifiers. Application and Performance Evaluations. Summary. References.; Appendix A--Matrix Algebra of Linear Transformation. Vectors. Matrices. The Data Matrix. Orthogonal Matrices and the Trace. Matrix Differentiation. Eigenvalues and Eigenvectors. Theorem of Spectral Decomposition. Theorem of Singular Value Decomposition. Quadratic Forms. Maximization and Minimization Theorem. References.; List of Figures.; Index.;