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    Digital filters : theory, application and design of modern filters / Rajiv J. Kapadia.

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    • Title:Digital filters : theory, application and design of modern filters / Rajiv J. Kapadia.
    •    
    • Author/Creator:Kapadia, Rajiv J., 1952-
    • Published/Created:Weinheim, Germany : Wiley-VCH, ©2012.

    • Holdings

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    • Library of Congress Subjects:Electric filters, Digital--Design and construction.
    • Description:xi, 359 p. : ill. ; 25 cm.
    • Notes:Includes bibliographical references and index.
    • ISBN:9783527411481 (pbk.)
      3527411488 (pbk.)
    • Contents:Machine generated contents note: 1. Background and Introduction
      1.1. Introduction
      1.2. How is Digital Processing Done?
      1.3. What is Filtering?
      1.3.1. Intersymbol Interference
      1.3.2. Noise
      1.4. Linear Filters
      1.4.1. FIR Filter
      1.4.2. IIR Filter
      1.4.3. How and Where Filters Operate
      1.5. Multirate Filters
      1.5.1. Altering the Sampling Rate by a Fraction
      1.5.2. Subband Decomposition
      1.6. Classical Filtering Model
      1.7. Optimum Solution to the Classical Problem
      1.7.1. Improving the Optimum Filter
      1.8. Classes of Applications of Adaptive Filters
      1.8.1. System Identification
      1.8.2. Inverse Modeling
      1.8.3. Prediction Modeling
      1.8.4. Interference Canceling
      1.9. Chapter Summary
      2. Discrete Time Signals and Systems
      2.1. Introduction
      2.1.1. Discrete Time Signals
      2.2. Operations on Signals
      2.3. Symmetry in Signals
      2.3.1. Odd and Even Sequences
      2.3.2. Conjugate Symmetric and Conjugate Antisymmetric Sequences
      2.4. Energy and Power Signals
      2.5. Concept of Frequency in Discrete Time Systems
      2.6. Discrete Time Systems
      2.6.1. Static versus Dynamic
      2.6.2. Time Variant versus Time Invariant
      2.6.3. Linear versus Nonlinear
      2.6.4. Causal versus Noncausal
      2.6.5. Stable versus Nonstable
      2.7. Analysis of Shift-Invariant Linear System
      2.7.1. Input Sequence as a Sum of Shifted Weighted Impulses
      2.7.2. Response to a Linear Shift Invariant System
      2.8. Convolution Sum
      2.8.1. Properties of Convolution
      2.8.1.1. Commutative Law
      2.8.1.2. Associative Law
      2.8.1.3. Distributive Law
      2.9. Systems Described by Difference Equations
      2.9.1. Systems Described by Constant Coefficient Difference Equation
      2.9.2. Solution of Linear Constant Coefficient Difference Equation
      2.9.3. Zero Input Response
      2.9.4. Zero State Response
      2.9.5. Complete Solution of the Difference Equation
      2.10. Impulse Response to a System
      2.11. Examples of Some Discrete Time Systems
      2.11.1. Accumulator
      2.11.2. Moving Average Filter
      2.11.3. Median Filter
      2.11.4. Linear Interpolator
      2.12. Chapter Summary
      3. Discrete Time Systems in the Frequency Domain
      3.1. Introduction
      3.2. Continuous Time Fourier Transform
      3.2.1. Definition of the Fourier Transform
      3.3. Sampling an Analog Signal
      3.4. Discrete Time Fourier Transform
      3.4.1. Definition of the Discrete Time Fourier Transform
      3.4.2. Properties of the DTFT
      3.4.2.1. Linearity
      3.4.2.2. Time Reversal
      3.4.2.3. Shift in the Time Domain
      3.4.2.4. Shift in the Frequency Domain
      3.4.2.5. Multiplication by a Linear Ramp
      3.4.2.6. Convolution in the Time Domain
      3.4.2.7. Parseval's Relation
      3.5. Sampling a Continuous Time Signal
      3.5.1. Nyquist Sampling Theorem
      3.5.2. Reconstruction of the Sampled Signal
      3.6. Discrete Fourier Transform
      3.6.1. Definition
      3.6.1.1. Computing the DFT from the Definition
      3.6.2. Relation between the DTFT and the DFT
      3.6.3. Relation between the Fourier Transform and the DFT
      3.7. Properties of the DFT
      3.7.1. Circular Shift
      3.7.2. Symmetry Relations in the DFT
      3.7.2.1. Real and Imaginary Parts of the DFT
      3.7.2.2. DFT of the Conjugate of x[n]
      3.7.2.3. DFT of the Time-Reversed Sequence
      3.7.2.4. DFT of the Real and the Imaginary Parts of the Sequence x[n]
      3.7.2.5. DFT of the Conjugate Symmetric and the Conjugate Antisymmetric Part of the Sequence x[n]
      3.8. Theorems of the DFT
      3.8.1. DFT is a Linear Transform
      3.8.2. DFT of a Circular Shift in Time
      3.8.3. IDFT of a Circular Shift in Frequency
      3.8.4. Circular Convolution
      3.8.5. Linear Convolution Using the Circular Convolution
      3.9. DFT of Real Sequences
      3.9.1. DFT of a 2N Point Real Sequence Using N Point DFT
      3.9.2. Two N Point DFT of Real Sequences Using a Single N Point DFT
      3.10. Convolution of Very Long Sequences
      3.10.1. Overlap and Add Method
      3.10.2. Overlap and Save Method
      3.11. Chapter Summary
      4. Z-Transform
      4.1. Introduction
      4.2. Definition of the Z-Transform
      4.2.1. Importance of the Region of Convergence
      4.2.2. Region of Convergence of Left- and Right-sided Sequences
      4.3. Inverse Z-Transform
      4.3.1. Cauchy Integral Theorem
      4.3.2. Partial Fraction Expansion
      4.3.2.1. Computing Residues Using MATLAB
      4.3.3. Long Division
      4.4. Theorems and Properties of the Z-Transform
      4.4.1. Region of Convergence
      4.4.2. Linearity
      4.4.3. Shift in the Time Domain
      4.4.4. Scaling in the Frequency Domain
      4.4.5. Conjugation of a Complex Sequence
      4.4.6. Differentiation in the Z-Domain
      4.4.7. Convolution of Two Time Domain Sequences
      4.4.8. Summary of Z-Transform Theorems and Properties
      4.5. Application of Z-Transforms to Systems
      4.6. Responses to Typical Pole-Zero Patterns
      4.6.1. First-Order Poles
      4.6.2. Second-Order Poles
      4.7. Introduction to Two-Dimensional Z-Transform
      4.8. Chapter Summary
      4.8.1. Definition of Z-Transform
      4.8.2. Inverse of the Z-Transform
      4.8.3. Theorems and Properties of the Z-Transform
      4.8.4. Application of Z-Transforms to Systems
      4.8.5. Responses to Typical Pole-Zero Patterns of Systems
      4.8.6. Introduction to Two-Dimensional Z-Transform
      5. Discrete Filter Design Techniques
      5.1. Introduction
      5.2. Design of Analog Filters: A Review
      5.2.1. Filter Specifications
      5.2.2. Butterworth Approximation
      5.2.3. Chebyshev Type 1 Approximation
      5.2.4. Chebyshev Type 2 Approximation
      5.2.5. Scaling the Filters
      5.2.6. Transforming Filters
      5.3. Design of IIR Filters from Analog Filters
      5.3.1. Impulse Invariance Method
      5.3.2. Bilinear Transform Method
      5.3.3. Frequency Transformations of IIR Discrete Filters
      5.4. Design of FIR Filters
      5.4.1. Linear Phase Transfer Functions
      5.4.2. Requirements of a Linear Phase Transfer Function
      5.4.3. Design of FIR Filters Using Windows
      5.4.4. Design of Filters Using Frequency Sampling
      5.4.5. Comparison of the FIR and the IIR Filters
      5.5. Design of Windows
      5.6. FIR Filter Design Using Optimization Techniques
      5.7. Chapter Summary
      6. Computing the DFT
      6.1. Introduction
      6.2. Direct Computation of the DFT
      6.3. Goertzel Algorithm
      6.4. Decimation in Time Algorithm
      6.5. Decimation in Frequency Algorithm
      6.6. Algorithm when N is a Composite Number
      6.7. Computing the FFT of Only a Few Samples
      6.8. Chirp Z-Algorithm
      6.9. Chapter Summary
      7. Multirate Signal Processing and Devices
      7.1. Introduction
      7.2. Time Domain Characteristics of the Sampling Rate Alteration Devices
      7.2.1. Upsampler
      7.2.2. Downsampler
      7.3. Frequency Domain Characteristics of the Sampling Rate Alteration Devices
      7.3.1. Upsampler
      7.3.2. Downsampler
      7.3.3. Upsampler-Downsampler Cascade Arrangement
      7.3.4. Noble Identities
      7.4. Basic Sampling Rate Converters
      7.4.1. Input-Output Relations of a Fraction Rate Structure
      7.4.2. Multistage Design of Fraction Rate Converter
      7.4.2.1. Single-Stage Design
      7.4.2.2. Multistage Design
      7.4.3. Application of Sampling Rate Converter
      7.5. Polyphase Decomposition
      7.6. Computationally Efficient Interpolator and Decimator
      7.6.1. Computationally Efficient Fraction Rate Converters
      7.6.2. Building an Efficient Fraction Rate Converter
      7.7. Half Band and Nyquist Filters
      7.7.1. Design of Linear Phase L-Band Filters
      7.8. Chapter Summary
      8. Introduction to Stochastic Processes
      8.1. Introduction
      8.2. Types of Random Variables, Expected Value, and Moments
      8.2.1. Continuous Random Variables
      8.2.2. Discrete Random Variables
      8.2.3. Mixed Random Variables
      8.2.4. Expected Value Operator
      8.2.5. Variance
      8.3. Correlation and Covariance
      8.3.1. Correlation
      8.3.2. Covariance
      8.3.3. Correlation Matrix
      8.3.4. Complex Valued Random Experiments
      8.4. Notion of the Stochastic Process
      8.4.1. Mean Value
      8.4.2. Autocorrelation
      8.4.3. Properties of Autocorrelation
      8.4.4. Autocovariance
      8.4.5. Stationary Process
      8.4.6. Ergodic Process
      8.4.7. Power Spectrum Density
      8.4.8. Properties of the Power Spectrum Density
      8.5. Correlation Matrix
      8.6. White Noise Process
      8.7. Stochastic Process through a Linear Shift-Invariant Filter
      8.8. Stochastic Models
      8.8.1. Autoregressive Model
      8.8.2. Moving Average Model
      8.8.3. Autoregressive Moving Average Process
      8.8.4. Correlation Function of a Stationary AR Process
      8.8.5. Yule-Walker Equations
      8.8.6. Relation between the Filter Parameters and the Autocorrelation Sequence
      8.9. Chapter Summary
      9. Weiner Filters
      9.1. Introduction
      9.2. Principle of Orthogonality
      9.3. Weiner-Hopf Equations
      9.4. Solution of the Weiner-Hopf Equations in the Time Domain
      9.4.1. Error Performance Surface
      9.4.2. Minimum Mean Square Error
      9.5. Solution of the Weiner-Hopf Equations in the Frequency Domain
      9.5.1. Innovation Representation of a Stochastic Process
      9.5.2. Solution to the Original Problem
      9.5.3. Minimum Mean Square Error
      9.5.3.1. Solution in the Frequency Domain
      9.5.3.2. Solution in the Time Domain
      9.6. Canonical Form of the Error Surface
      9.7. Weiner Filters with Additional Constraints
      9.8. Chapter Summary
      Contents note continued: 10. Adaptive Filters
      10.1. Introduction
      10.1.1. Applications of Adaptive Filters
      10.1.2. System Identification
      10.1.3. Inverse Modeling
      10.1.4. Prediction
      10.1.5. Interference Canceling
      10.2. Adaptive Direct Form FIR Filters
      10.3. Gradient Algorithm
      10.3.1. Method of Steepest Descent
      10.4. Other Related Stochastic Gradient Algorithms
      10.4.1. Average Stochastic Gradient Algorithm
      10.4.2. Low-Pass Filter of the Gradient
      10.4.3. Conjugate Gradient Algorithm
      10.4.4. Error Sign Algorithm
      10.4.5. Normalized LMS Algorithm
      10.5. Properties of the Gradient Algorithms
      10.5.1. Examples of Adaptive Filters Using the LMS Algorithm
      10.5.2. Computing Time to Convergence
      10.5.3. Summary of the LMS Algorithm
      10.6. Recursive Least Squares Algorithm
      10.6.1. Definitions
      10.6.2. Recursive Computation of DM(n) and Γxx
      10.6.3. RLS Algorithm
      10.6.4. Summary of the RLS Algorithm
      10.7. Chapter Summary
      Further Reading
      Appendix A Mathematical Identities
      Appendix B Transform Tables
      B.1. Fourier Series
      B.2. Fourier Transform
      B.3. Laplace Transform
      B.4. Z-Transform
      B.5. Discrete Fourier Transform
      Appendix C Introduction to MATLAB
      C.1. Introduction
      C.2. Numbers and Data Representation
      C.3. Control Flow
      C.4. Special Operators and Predefined Variables
      C.5. Drawing Plots in MATLAB
      C.6. Some Special Commands Used in this Book.
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