mohamed najim - digital filters design for signal and image processing

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mohamed najim  -  digital filters design for signal and image processing

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[...]... Magnitude and Delay Approximation of 1-D and 2-D Digital Filters, Springer, 1999, ISBN 3-5 4 0-6 416 1-0 [THE 92] THERRIEN C., Discrete Random Signals and Statistical Signal Processing, Prentice Hall, ISBN 0-1 3-8 5211 2-3 , 1992 [TRE 76] TREITTER S A., Introduction to Discrete-Time Signal Processing, John Wiley & Sons (Sd), 1976, ISBN 0-4 7 1-8 876 0-9 [VAN 89] VAN DEN ENDEN A W M and VERHOECKX N A M., Discrete-Time Signal. .. Boston, ISBN 0-8 983 8-1 7 4-6 1986 [KAL 97] KALOUPTSIDIS N., Signal Processing Systems, Theory and Design, Wiley Interscience, 1997, ISBN 0-4 7 1-1 122 0-8 [ORF 96] ORFANIDIS S J., Introduction to Signal Processing, Prentice Hall, ISBN 0-1 320917 2-0 , 1996 [PRO 92] PROAKIS J and MANOLAKIS D., Digital Signal Processing, Principles, Algorithms and Applications, 2nd ed., MacMillan, 1992, ISBN 0-0 2-3 96815-X [SHE 99] SHENOI... ≥ 0 ⎪ Unit step signal: ⎨ ⎪u ( k ) = 0 for k < 0 ⎩ ⎧ r ( k ) = k for k ≥ 0 ⎪ Unit ramp signal: ⎨ ⎪r ( k ) = 0 for k < 0 ⎩ impulse unity amplitude 1 0.8 0.6 0.4 0.2 0 -1 0 -8 -6 -4 -2 0 Scale unity 2 4 6 8 10 -8 -6 -4 -2 0 indices 2 4 6 8 10 amplitude 1 0.8 0.6 0.4 0.2 0 -1 0 Figure 1.4 Unit sample sequence δ(k) and unit step signal u(k) 1.2.2 Deterministic and random signals We class signals as being... systems It discusses the time-domain representations and characterizations of the continuoustime and discrete-time signals Chapter 2 details the background for the analysis of discrete-time signals It mainly deals with the z-transform, its properties and its use for the analysis of linear systems, represented by difference equations xiv Digital Filters Design for Signal and Image Processing Chapter 3 is... x(t) then depends on the statistical properties of these random variables 8 Digital Filters Design for Signal and Image Processing Figure 1.6 Several examples of a discrete random 2-D process 1.2.3 Periodic signals The class of signals termed periodic plays an important role in signal and image processing In the case of a continuous-time signal, a signal is called periodic of period T0 if T0 is the smallest... representations and characterizations 1.2.1 Definition of continuous-time and discrete-time signals The function of a signal is to serve as a medium for information It is a representation of the variations of a physical variable Chapter written by Yannick BERTHOUMIEU, Eric GRIVEL and Mohamed NAJIM 2 Digital Filters Design for Signal and Image Processing A signal can be measured by a sensor, then analyzed to describe... role Introduction to Signals and Systems 5 Physical variable Sensor Analog signal Adaptation amplifier Processed signal Low-pass filter or pass-band Smoothing filter Sampling blocker Digital system A/D converter Digital input signal Processing D/A converter Digital output signal Figure 1.3 Complete acquisition chain and digital processing of a signal Different types of digital signal representation... dedicated to digital filtering, this title features both 1-D and 2-D systems, and as such covers both signal and image processing Thus, in Chapters 8 and 9, 2-D filtering is investigated Moreover, it is not easy to establish the necessary and sufficient conditions to test the stability of 2-D signals Therefore, Chapters 10 and 11 are dedicated to the difficult problem of the stability of 2-D digital system,... last decade, digital signal processing has matured; thus, digital signal processing techniques have played a key role in the expansion of electronic products for everyday use, especially in the field of audio, image and video processing Nowadays, digital signal is used in MP3 and DVD players, digital cameras, mobile phones, and also in radar processing, biomedical applications, seismic data processing, ... thorough introduction to digital signal processing featuring the design of digital filters The purpose of the first part (Chapters 1 to 9) is to initiate the newcomer to digital signal and image processing whereas the second part (Chapters 10 and 11) covers some advanced topics on stability for 2-D filter design These chapters are written at a level that is suitable for students or for individual study . index. ISBN-13: 97 8-1 -9 0520 9-4 5-3 ISBN-10: 1-9 0520 9-4 5-2 1. Electric filters, Digital. 2. Signal processing Digital techniques. 3. Image processing Digital techniques. I. Najim, Mohamed. . alt="" Digital Filters Design for Signal and Image Processing This page intentionally left blank Digital Filters Design for Signal and Image Processing Edited by Mohamed. Cataloging-in-Publication Data Synthèse de filtres numériques en traitement du signal et des images. English Digital filters design for signal and image processing/ edited by Mohamed Najim.

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  • Table of Contents

  • Introduction

  • Chapter 1. Introduction to Signals and Systems

    • 1.1. Introduction

    • 1.2. Signals: categories, representations and characterizations

      • 1.2.1. Definition of continuous-time and discrete-time signals

      • 1.2.2. Deterministic and random signals

      • 1.2.3. Periodic signals

      • 1.2.4. Mean, energy and power

      • 1.2.5. Autocorrelation function

    • 1.3. Systems

    • 1.4. Properties of discrete-time systems

      • 1.4.1. Invariant linear systems

      • 1.4.2. Impulse responses and convolution products

      • 1.4.3. Causality

      • 1.4.4. Interconnections of discrete-time systems

    • 1.5. Bibliography

  • Chapter 2. Discrete System Analysis

    • 2.1. Introduction

    • 2.2. The z-transform

      • 2.2.1. Representations and summaries

      • 2.2.2. Properties of the z-transform

      • 2.2.3. Table of standard transform

    • 2.3. The inverse z-transform

      • 2.3.1. Introduction

      • 2.3.2. Methods of determining inverse z-transforms

    • 2.4. Transfer functions and difference equations

      • 2.4.1. The transfer function of a continuous system

      • 2.4.2. Transfer functions of discrete systems

    • 2.5. Z-transforms of the autocorrelation and intercorrelation functions

    • 2.6. Stability

      • 2.6.1. Bounded input, bounded output (BIBO) stability

      • 2.6.2. Regions of convergence

  • Chapter 3. Frequential Characterization of Signals and Filters

    • 3.1. Introduction

    • 3.2. The Fourier transform of continuous signals

      • 3.2.1. Summary of the Fourier series decomposition of continuous signals

      • 3.2.2. Fourier transforms and continuous signals

    • 3.3. The discrete Fourier transform (DFT)

      • 3.3.1. Expressing the Fourier transform of a discrete sequence

      • 3.3.2. Relations between the Laplace and Fourier z-transforms

      • 3.3.3. The inverse Fourier transform

      • 3.3.4. The discrete Fourier transform

    • 3.4. The fast Fourier transform (FFT)

    • 3.5. The fast Fourier transform for a time/frequency/energy representation of a non-stationary signal

    • 3.6. Frequential characterization of a continuous-time system

      • 3.6.1. First and second order filters

    • 3.7. Frequential characterization of discrete-time system

      • 3.7.1. Amplitude and phase frequential diagrams

      • 3.7.2. Application

  • Chapter 4. Continuous-Time and Analog Filters

    • 4.1. Introduction

    • 4.2. Different types of filters and filter specifications

    • 4.3. Butterworth filters and the maximally flat approximation

      • 4.3.1. Maximally flat functions (MFM)

      • 4.3.2. A specific example of MFM functions: Butterworth polynomial filters

    • 4.4. Equiripple filters and the Chebyshev approximation

      • 4.4.1. Characteristics of the Chebyshev approximation

      • 4.4.2. Type I Chebyshev filters

      • 4.4.3. Type II Chebyshev filter

    • 4.5. Elliptic filters: the Cauer approximation

    • 4.6. Summary of four types of low-pass filter: Butterworth, Chebyshev type I, Chebyshev type II and Cauer

    • 4.7. Linear phase filters (maximally flat delay or MFD): Bessel and Thomson filters

      • 4.7.1. Reminders on continuous linear phase filters

      • 4.7.2. Properties of Bessel-Thomson filters

      • 4.7.3. Bessel and Bessel-Thomson filters

    • 4.8. Papoulis filters (optimum (O[sub(n)]))

      • 4.8.1. General characteristics

      • 4.8.2. Determining the poles of the transfer function

    • 4.9. Bibliography

  • Chapter 5. Finite Impulse Response Filters

    • 5.1. Introduction to finite impulse response filters

      • 5.1.1. Difference equations and FIR filters

      • 5.1.2. Linear phase FIR filters

      • 5.1.3. Summary of the properties of FIR filters

    • 5.2. Synthesizing FIR filters using frequential specifications

      • 5.2.1. Windows

      • 5.2.2. Synthesizing FIR filters using the windowing method

    • 5.3. Optimal approach of equal ripple in the stop-band and passband

    • 5.4. Bibliography

  • Chapter 6. Infinite Impulse Response Filters

    • 6.1. Introduction to infinite impulse response filters

      • 6.1.1. Examples of IIR filters

      • 6.1.2. Zero-loss and all-pass filters

      • 6.1.3. Minimum-phase filters

    • 6.2. Synthesizing IIR filters

      • 6.2.1. Impulse invariance method for analog to digital filter conversion

      • 6.2.2. The invariance method of the indicial response

      • 6.2.3. Bilinear transformations

      • 6.2.4. Frequency transformations for filter synthesis using low-pass filters

    • 6.3. Bibliography

  • Chapter 7. Structures of FIR and IIR Filters

    • 7.1. Introduction

    • 7.2. Structure of FIR filters

    • 7.3. Structure of IIR filters

      • 7.3.1. Direct structures

      • 7.3.2. The cascade structure

      • 7.3.3. Parallel structures

    • 7.4. Realizing finite precision filters

      • 7.4.1. Introduction

      • 7.4.2. Examples of FIR filters

      • 7.4.3. IIR filters

    • 7.5. Bibliography

  • Chapter 8. Two-Dimensional Linear Filtering

    • 8.1. Introduction

    • 8.2. Continuous models

      • 8.2.1. Representation of 2-D signals

      • 8.2.2. Analog filtering

    • 8.3. Discrete models

      • 8.3.1. 2-D sampling

      • 8.3.2. The aliasing phenomenon and Shannon's theorem

    • 8.4. Filtering in the spatial domain

      • 8.4.1. 2-D discrete convolution

      • 8.4.2. Separable filters

      • 8.4.3. Separable recursive filtering

      • 8.4.4. Processing of side effects

    • 8.5. Filtering in the frequency domain

      • 8.5.1. 2-D discrete Fourier transform (DFT)

      • 8.5.2. The circular convolution effect

    • 8.6. Bibliography

  • Chapter 9. Two-Dimensional Finite Impulse Response Filter Design

    • 9.1. Introduction

    • 9.2. Introduction to 2-D FIR filters

    • 9.3. Synthesizing with the two-dimensional windowing method

      • 9.3.1. Principles of method

      • 9.3.2. Theoretical 2-D frequency shape

      • 9.3.3. Digital 2-D filter design by windowing

      • 9.3.4. Applying filters based on rectangular and circular shapes

      • 9.3.5. 2-D Gaussian filters

      • 9.3.6. 1-D and 2-D representations in a continuous space

      • 9.3.7. Approximation for FIR filters

      • 9.3.8. An example based on exploiting a modulated Gaussian filter

    • 9.4. Appendix: spatial window functions and their implementation

    • 9.5. Bibliography

  • Chapter 10. Filter Stability

    • 10.1. Introduction

    • 10.2. The Schur-Cohn criterion

    • 10.3. Appendix: resultant of two polynomials

    • 10.4. Bibliography

  • Chapter 11. The Two-Dimensional Domain

    • 11.1. Recursive filters

      • 11.1.1. Transfer functions

      • 11.1.2. The 2-D z-transform

      • 11.1.3. Stability, causality and semi-causality

    • 11.2. Stability criteria

      • 11.2.1. Causal filters

      • 11.2.2. Semi-causal filters

    • 11.3. Algorithms used in stability tests

      • 11.3.1. The jury Table

      • 11.3.2. Algorithms based on calculating the Bezout resultant

      • 11.3.3. Algorithms and rounding-off errors

    • 11.4. Linear predictive coding

    • 11.5. Appendix A: demonstration of the Schur-Cohn criterion

    • 11.6. Appendix B: optimum 2-D stability criteria

    • 11.7. Bibliography

  • List of Authors

  • Index

    • A

    • B

    • C

    • D

    • E

    • F

    • I

    • L

    • M

    • O

    • P

    • R

    • S

    • T

    • U

    • W

    • Z

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