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Digital Filters Design for Signal and Image Processing

Book Description

Dealing with digital filtering methods for 1-D and 2-D signals, this book provides the theoretical background in signal processing, covering topics such as the z-transform, Shannon sampling theorem and fast Fourier transform. An entire chapter is devoted to the design of time-continuous filters which provides a useful preliminary step for analog-to-digital filter conversion.

Attention is also given to the main methods of designing finite impulse response (FIR) and infinite impulse response (IIR) filters. Bi-dimensional digital filtering (image filtering) is investigated and a study on stability analysis, a very useful tool when implementing IIR filters, is also carried out. As such, it will provide a practical and useful guide to those engaged in signal processing.

Table of Contents

  1. Cover Page
  2. Title Page
  3. Copyright
  4. Contents
  5. Introduction
  6. Chapter 1: Introduction to Signals and Systems
    1. 1.1. Introduction
    2. 1.2. Signals: categories, representations and characterizations
    3. 1.3. Systems
    4. 1.4. Properties of discrete-time systems
    5. 1.5. Bibliography
  7. Chapter 2: Discrete System Analysis
    1. 2.1. Introduction
    2. 2.2. The z-transform
    3. 2.3. The inverse z-transform
    4. 2.4. Transfer functions and difference equations
    5. 2.5. Z-transforms of the autocorrelation and intercorrelation functions
    6. 2.6. Stability
  8. Chapter 3: Frequential Characterization of Signals and Filters
    1. 3.1. Introduction
    2. 3.2. The Fourier transform of continuous signals
    3. 3.3. The discrete Fourier transform (DFT)
    4. 3.4. The fast Fourier transform (FFT)
    5. 3.5. The fast Fourier transform for a time/frequency/energy representation of a non-stationary signal
    6. 3.6. Frequential characterization of a continuous-time system
    7. 3.7. Frequential characterization of discrete-time system
  9. Chapter 4: Continuous-Time and Analog Filters
    1. 4.1. Introduction
    2. 4.2. Different types of filters and filter specifications
    3. 4.3. Butterworth filters and the maximally flat approximation
    4. 4.4. Equiripple filters and the Chebyshev approximation
    5. 4.5. Elliptic filters: the Cauer approximation
    6. 4.6. Summary of four types of low-pass fllter: Butterworth, Chebyshev type I, Chebyshev type II and Cauer
    7. 4.7. Linear phase filters (maximally flat delay or MFD): Bessel and Thomson filters
    8. 4.8. Papoulis filters (optimum (O n ))
    9. 4.9. Bibliography
  10. Chapter 5: Finite Impulse Response Filters
    1. 5.1. Introduction to finite impulse response filters
    2. 5.2. Synthesizing FIR filters using frequential specifications
    3. 5.3. Optimal approach of equal ripple in the stop-band and passband
    4. 5.4. Bibliography
  11. Chapter 6: Infinite Impulse Response Filters
    1. 6.1. Introduction to infinite impulse response filters
    2. 6.2. Synthesizing IIR filters
    3. 6.3. Bibliography
  12. Chapter 7: Structures of FIR and IIR Filters
    1. 7.1. Introduction
    2. 7.2. Structure of FIR filters
    3. 7.3. Structure of IIR filters
    4. 7.4. Realizing finite precision filters
    5. 7.5. Bibliography
  13. Chapter 8: Two-Dimensional Linear Filtering
    1. 8.1. Introduction
    2. 8.2. Continuous models
    3. 8.3. Discrete models
    4. 8.4. Filtering in the spatial domain
    5. 8.5. Filtering in the frequency domain
    6. 8.6. Bibliography
  14. Chapter 9: Two-Dimensional Finite Impulse Response Filter Design
    1. 9.1. Introduction
    2. 9.2. Introduction to 2-D FIR filters
    3. 9.3. Synthesizing with the two-dimensional windowing method
    4. 9.4. Appendix: spatial window functions and their implementation
    5. 9.5. Bibliography
  15. Chapter 10: Filter Stability
    1. 10.1. Introduction
    2. 10.2. The Schur-Cohn criterion
    3. 10.3. Appendix: resultant of two polynomials
    4. 10.4. Bibliography
  16. Chapter 11: The Two-Dimensional Domain
    1. 11.1. Recursive filters
    2. 11.2. Stability criteria
    3. 11.3. Algorithms used in stability tests
    4. 11.4. Linear predictive coding
    5. 11.5. Appendix A: demonstration of the Schur-Cohn criterion
    6. 11.6. Appendix B: optimum 2-D stability criteria
    7. 11.7. Bibliography
  17. List of Authors
  18. INDEX