{"product_id":"digital-filters-design-for-signal-and-image-processing-isbn-9781905209453","title":"Digital Filters Design for Signal and Image Processing","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.\u003cbr\u003e 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.  \u003cp\u003e\u003ci\u003eIntroduction xiii\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 1. Introduction to Signals and Systems 1\u003c\/b\u003e\u003cbr\u003e \u003ci\u003eYannick BERTHOUMIEU, Eric GRIVEL and Mohamed NAJIM\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e1.1. Introduction 1\u003c\/p\u003e \u003cp\u003e1.2. Signals: categories, representations and characterizations 1\u003c\/p\u003e \u003cp\u003e1.2.1. Definition of continuous-time and discrete-time signals 1\u003c\/p\u003e \u003cp\u003e1.2.2. Deterministic and random signals 6\u003c\/p\u003e \u003cp\u003e1.2.3. Periodic signals 8\u003c\/p\u003e \u003cp\u003e1.2.4. Mean, energy and power 9\u003c\/p\u003e \u003cp\u003e1.2.5. Autocorrelation function 12\u003c\/p\u003e \u003cp\u003e1.3. Systems 15\u003c\/p\u003e \u003cp\u003e1.4. Properties of discrete-time systems 16\u003c\/p\u003e \u003cp\u003e1.4.1. Invariant linear systems 16\u003c\/p\u003e \u003cp\u003e1.4.2. Impulse responses and convolution products 16\u003c\/p\u003e \u003cp\u003e1.4.3. Causality 17\u003c\/p\u003e \u003cp\u003e1.4.4. Interconnections of discrete-time systems 18\u003c\/p\u003e \u003cp\u003e1.5. Bibliography 19\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 2. Discrete System Analysis 21\u003c\/b\u003e\u003cbr\u003e \u003ci\u003eMohamed NAJIM and Eric GRIVEL\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e2.1. Introduction 21\u003c\/p\u003e \u003cp\u003e2.2. The z-transform 21\u003c\/p\u003e \u003cp\u003e2.2.1. Representations and summaries 21\u003c\/p\u003e \u003cp\u003e2.2.2. Properties of the z-transform 28\u003c\/p\u003e \u003cp\u003e2.2.2.1. Linearity 28\u003c\/p\u003e \u003cp\u003e2.2.2.2. Advanced and delayed operators 29\u003c\/p\u003e \u003cp\u003e2.2.2.3. Convolution 30\u003c\/p\u003e \u003cp\u003e2.2.2.4. Changing the z-scale 31\u003c\/p\u003e \u003cp\u003e2.2.2.5. Contrasted signal development 31\u003c\/p\u003e \u003cp\u003e2.2.2.6. Derivation of the z-transform 31\u003c\/p\u003e \u003cp\u003e2.2.2.7. The sum theorem 32\u003c\/p\u003e \u003cp\u003e2.2.2.8. The final-value theorem 32\u003c\/p\u003e \u003cp\u003e2.2.2.9. Complex conjugation 32\u003c\/p\u003e \u003cp\u003e2.2.2.10. Parseval’s theorem 33\u003c\/p\u003e \u003cp\u003e2.2.3. Table of standard transform 33\u003c\/p\u003e \u003cp\u003e2.3. The inverse z-transform 34\u003c\/p\u003e \u003cp\u003e2.3.1. Introduction 34\u003c\/p\u003e \u003cp\u003e2.3.2. Methods of determining inverse z-transforms 35\u003c\/p\u003e \u003cp\u003e2.3.2.1. Cauchy’s theorem: a case of complex variables 35\u003c\/p\u003e \u003cp\u003e2.3.2.2. Development in rational fractions 37\u003c\/p\u003e \u003cp\u003e2.3.2.3. Development by algebraic division of polynomials 38\u003c\/p\u003e \u003cp\u003e2.4. Transfer functions and difference equations 39\u003c\/p\u003e \u003cp\u003e2.4.1. The transfer function of a continuous system 39\u003c\/p\u003e \u003cp\u003e2.4.2. Transfer functions of discrete systems 41\u003c\/p\u003e \u003cp\u003e2.5. Z-transforms of the autocorrelation and intercorrelation functions 44\u003c\/p\u003e \u003cp\u003e2.6. Stability 45\u003c\/p\u003e \u003cp\u003e2.6.1. Bounded input, bounded output (BIBO) stability 46\u003c\/p\u003e \u003cp\u003e2.6.2. Regions of convergence 46\u003c\/p\u003e \u003cp\u003e2.6.2.1. Routh’s criterion 48\u003c\/p\u003e \u003cp\u003e2.6.2.2. Jury’s criterion 49\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 3. Frequential Characterization of Signals and Filters 51\u003c\/b\u003e\u003cbr\u003e \u003ci\u003eEric GRIVEL and Yannick BERTHOUMIEU\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e3.1. Introduction 51\u003c\/p\u003e \u003cp\u003e3.2. The Fourier transform of continuous signals 51\u003c\/p\u003e \u003cp\u003e3.2.1. Summary of the Fourier series decomposition of continuous signals 51\u003c\/p\u003e \u003cp\u003e3.2.1.1. Decomposition of finite energy signals using an orthonormal base 51\u003c\/p\u003e \u003cp\u003e3.2.1.2. Fourier series development of periodic signals 52\u003c\/p\u003e \u003cp\u003e3.2.2. Fourier transforms and continuous signals 57\u003c\/p\u003e \u003cp\u003e3.2.2.1. Representations 57\u003c\/p\u003e \u003cp\u003e3.2.2.2. Properties 58\u003c\/p\u003e \u003cp\u003e3.2.2.3. The duality theorem 59\u003c\/p\u003e \u003cp\u003e3.2.2.4. The quick method of calculating the Fourier transform 59\u003c\/p\u003e \u003cp\u003e3.2.2.5. The Wiener-Khintchine theorem 63\u003c\/p\u003e \u003cp\u003e3.2.2.6. The Fourier transform of a Dirac comb 63\u003c\/p\u003e \u003cp\u003e3.2.2.7. Another method of calculating the Fourier series development of a periodic signal 66\u003c\/p\u003e \u003cp\u003e3.2.2.8. The Fourier series development and the Fourier transform 68\u003c\/p\u003e \u003cp\u003e3.2.2.9. Applying the Fourier transform: Shannon’s sampling theorem 75\u003c\/p\u003e \u003cp\u003e3.3. The discrete Fourier transform (DFT) 78\u003c\/p\u003e \u003cp\u003e3.3.1. Expressing the Fourier transform of a discrete sequence 78\u003c\/p\u003e \u003cp\u003e3.3.2. Relations between the Laplace and Fourier z-transforms 80\u003c\/p\u003e \u003cp\u003e3.3.3. The inverse Fourier transform 81\u003c\/p\u003e \u003cp\u003e3.3.4. The discrete Fourier transform 82\u003c\/p\u003e \u003cp\u003e3.4. The fast Fourier transform (FFT) 86\u003c\/p\u003e \u003cp\u003e3.5. The fast Fourier transform for a time\/frequency\/energy representation of a non-stationary signal 90\u003c\/p\u003e \u003cp\u003e3.6. Frequential characterization of a continuous-time system 91\u003c\/p\u003e \u003cp\u003e3.6.1. First and second order filters 91\u003c\/p\u003e \u003cp\u003e3.6.1.1. 1st order system 91\u003c\/p\u003e \u003cp\u003e3.6.1.2. 2nd order system 93\u003c\/p\u003e \u003cp\u003e3.7. Frequential characterization of discrete-time system 95\u003c\/p\u003e \u003cp\u003e3.7.1. Amplitude and phase frequential diagrams 95\u003c\/p\u003e \u003cp\u003e3.7.2. Application 96\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 4. Continuous-Time and Analog Filters 99\u003c\/b\u003e\u003cbr\u003e \u003ci\u003eDaniel BASTARD and Eric GRIVEL\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e4.1. Introduction 99\u003c\/p\u003e \u003cp\u003e4.2. Different types of filters and filter specifications 99\u003c\/p\u003e \u003cp\u003e4.3. Butterworth filters and the maximally flat approximation 104\u003c\/p\u003e \u003cp\u003e4.3.1. Maximally flat functions (MFM) 104\u003c\/p\u003e \u003cp\u003e4.3.2. A specific example of MFM functions: Butterworth polynomial filters 106\u003c\/p\u003e \u003cp\u003e4.3.2.1. Amplitude-squared expression 106\u003c\/p\u003e \u003cp\u003e4.3.2.2. Localization of poles 107\u003c\/p\u003e \u003cp\u003e4.3.2.3. Determining the cut-off frequency at –3 dB and filter orders 110\u003c\/p\u003e \u003cp\u003e4.3.2.4. Application 111\u003c\/p\u003e \u003cp\u003e4.3.2.5. Realization of a Butterworth filter 112\u003c\/p\u003e \u003cp\u003e4.4. Equiripple filters and the Chebyshev approximation 113\u003c\/p\u003e \u003cp\u003e4.4.1. Characteristics of the Chebyshev approximation 113\u003c\/p\u003e \u003cp\u003e4.4.2. Type I Chebyshev filters 114\u003c\/p\u003e \u003cp\u003e4.4.2.1. The Chebyshev polynomial 114\u003c\/p\u003e \u003cp\u003e4.4.2.2. Type I Chebyshev filters 115\u003c\/p\u003e \u003cp\u003e4.4.2.3. Pole determination 116\u003c\/p\u003e \u003cp\u003e4.4.2.4. Determining the cut-off frequency at –3 dB and the filter order 118\u003c\/p\u003e \u003cp\u003e4.4.2.5. Application 121\u003c\/p\u003e \u003cp\u003e4.4.2.6. Realization of a Chebyshev filter 121\u003c\/p\u003e \u003cp\u003e4.4.2.7. Asymptotic behavior 122\u003c\/p\u003e \u003cp\u003e4.4.3. Type II Chebyshev filter 123\u003c\/p\u003e \u003cp\u003e4.4.3.1. Determining the filter order and the cut-off frequency 123\u003c\/p\u003e \u003cp\u003e4.4.3.2. Application 124\u003c\/p\u003e \u003cp\u003e4.5. Elliptic filters: the Cauer approximation 125\u003c\/p\u003e \u003cp\u003e4.6. Summary of four types of low-pass filter: Butterworth, Chebyshev type I, Chebyshev type II and Cauer 125\u003c\/p\u003e \u003cp\u003e4.7. Linear phase filters (maximally flat delay or MFD): Bessel and Thomson filters 126\u003c\/p\u003e \u003cp\u003e4.7.1. Reminders on continuous linear phase filters 126\u003c\/p\u003e \u003cp\u003e4.7.2. Properties of Bessel-Thomson filters 128\u003c\/p\u003e \u003cp\u003e4.7.3. Bessel and Bessel-Thomson filters 130\u003c\/p\u003e \u003cp\u003e4.8. Papoulis filters (optimum (On)) 132\u003c\/p\u003e \u003cp\u003e4.8.1. General characteristics 132\u003c\/p\u003e \u003cp\u003e4.8.2. Determining the poles of the transfer function 135\u003c\/p\u003e \u003cp\u003e4.9. Bibliography 135\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 5. Finite Impulse Response Filters 137\u003c\/b\u003e\u003cbr\u003e \u003ci\u003eYannick BERTHOUMIEU, Eric GRIVEL and Mohamed NAJIM\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e5.1. Introduction to finite impulse response filters 137\u003c\/p\u003e \u003cp\u003e5.1.1. Difference equations and FIR filters 137\u003c\/p\u003e \u003cp\u003e5.1.2. Linear phase FIR filters 142\u003c\/p\u003e \u003cp\u003e5.1.2.1. Representation 142\u003c\/p\u003e \u003cp\u003e5.1.2.2. Different forms of FIR linear phase filters 147\u003c\/p\u003e \u003cp\u003e5.1.2.3. Position of zeros in FIR filters 150\u003c\/p\u003e \u003cp\u003e5.1.3. Summary of the properties of FIR filters 152\u003c\/p\u003e \u003cp\u003e5.2. Synthesizing FIR filters using frequential specifications 152\u003c\/p\u003e \u003cp\u003e5.2.1. Windows 152\u003c\/p\u003e \u003cp\u003e5.2.2. Synthesizing FIR filters using the windowing method 159\u003c\/p\u003e \u003cp\u003e5.2.2.1. Low-pass filters 159\u003c\/p\u003e \u003cp\u003e5.2.2.2. High-pass filters 164\u003c\/p\u003e \u003cp\u003e5.3. Optimal approach of equal ripple in the stop-band and passband 165\u003c\/p\u003e \u003cp\u003e5.4. Bibliography 172\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 6. Infinite Impulse Response Filters 173\u003c\/b\u003e\u003cbr\u003e \u003ci\u003eEric GRIVEL and Mohamed NAJIM\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e6.1. Introduction to infinite impulse response filters 173\u003c\/p\u003e \u003cp\u003e6.1.1. Examples of IIR filters 174\u003c\/p\u003e \u003cp\u003e6.1.2. Zero-loss and all-pass filters 178\u003c\/p\u003e \u003cp\u003e6.1.3. Minimum-phase filters180\u003c\/p\u003e \u003cp\u003e6.1.3.1. Problem 180\u003c\/p\u003e \u003cp\u003e6.1.3.2. Stabilizing inverse filters 181\u003c\/p\u003e \u003cp\u003e6.2. Synthesizing IIR filters 183\u003c\/p\u003e \u003cp\u003e6.2.1. Impulse invariance method for analog to digital filter conversion 183\u003c\/p\u003e \u003cp\u003e6.2.2. The invariance method of the indicial response 185\u003c\/p\u003e \u003cp\u003e6.2.3. Bilinear transformations 185\u003c\/p\u003e \u003cp\u003e6.2.4. Frequency transformations for filter synthesis using low-pass filters 188\u003c\/p\u003e \u003cp\u003e6.3. Bibliography 189\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 7. Structures of FIR and IIR Filters 191\u003c\/b\u003e\u003cbr\u003e \u003ci\u003eMohamed NAJIM and Eric GRIVEL\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e7.1. Introduction 191\u003c\/p\u003e \u003cp\u003e7.2. Structure of FIR filters 192\u003c\/p\u003e \u003cp\u003e7.3. Structure of IIR filters 192\u003c\/p\u003e \u003cp\u003e7.3.1. Direct structures 192\u003c\/p\u003e \u003cp\u003e7.32. The cascade structure 209\u003c\/p\u003e \u003cp\u003e7.3.3. Parallel structures 211\u003c\/p\u003e \u003cp\u003e7.4. Realizing finite precision filters 211\u003c\/p\u003e \u003cp\u003e7.4.1. Introduction 211\u003c\/p\u003e \u003cp\u003e7.4.2. Examples of FIR filters 212\u003c\/p\u003e \u003cp\u003e7.4.3. IIR filters 213\u003c\/p\u003e \u003cp\u003e7.4.3.1. Introduction 213\u003c\/p\u003e \u003cp\u003e7.4.3.2. The influence of quantification on filter stability 221\u003c\/p\u003e \u003cp\u003e7.4.3.3. Introduction to scale factors 224\u003c\/p\u003e \u003cp\u003e7.4.3.4. Decomposing the transfer function into first- and second-order cells 226\u003c\/p\u003e \u003cp\u003e7.5. Bibliography 231\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 8. Two-Dimensional Linear Filtering 233\u003c\/b\u003e\u003cbr\u003e \u003ci\u003ePhilippe BOLON\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e8.1. Introduction 233\u003c\/p\u003e \u003cp\u003e8.2. Continuous models 233\u003c\/p\u003e \u003cp\u003e8.2.1. Representation of 2-D signals 233\u003c\/p\u003e \u003cp\u003e8.2.2. Analog filtering 235\u003c\/p\u003e \u003cp\u003e8.3. Discrete models 236\u003c\/p\u003e \u003cp\u003e8.3.1. 2-D sampling 236\u003c\/p\u003e \u003cp\u003e8.3.2. The aliasing phenomenon and Shannon’s theorem 240\u003c\/p\u003e \u003cp\u003e8.3.2.1. Reconstruction by linear filtering (Shannon’s theorem) 240\u003c\/p\u003e \u003cp\u003e8.3.2.2. Aliasing effect 240\u003c\/p\u003e \u003cp\u003e8.4. Filtering in the spatial domain 242\u003c\/p\u003e \u003cp\u003e8.4.1. 2-D discrete convolution 242\u003c\/p\u003e \u003cp\u003e8.4.2. Separable filters 244\u003c\/p\u003e \u003cp\u003e8.4.3. Separable recursive filtering 246\u003c\/p\u003e \u003cp\u003e8.4.4. Processing of side effects 249\u003c\/p\u003e \u003cp\u003e8.4.4.1. Prolonging the image by pixels of null intensity 250\u003c\/p\u003e \u003cp\u003e8.4.4.2. Prolonging by duplicating the border pixels 251\u003c\/p\u003e \u003cp\u003e8.4.4.3. Other approaches 252\u003c\/p\u003e \u003cp\u003e8.5. Filtering in the frequency domain 253\u003c\/p\u003e \u003cp\u003e8.5.1. 2-D discrete Fourier transform (DFT) 253\u003c\/p\u003e \u003cp\u003e8.5.2. The circular convolution effect 255\u003c\/p\u003e \u003cp\u003e8.6. Bibliography 259\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 9. Two-Dimensional Finite Impulse Response Filter Design 261\u003c\/b\u003e\u003cbr\u003e \u003ci\u003eYannick BERTHOUMIEU\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e9.1. Introduction 261\u003c\/p\u003e \u003cp\u003e9.2. Introduction to 2-D FIR filters 262\u003c\/p\u003e \u003cp\u003e9.3. Synthesizing with the two-dimensional windowing method 263\u003c\/p\u003e \u003cp\u003e9.3.1. Principles of method 263\u003c\/p\u003e \u003cp\u003e9.3.2. Theoretical 2-D frequency shape 264\u003c\/p\u003e \u003cp\u003e9.3.2.1. Rectangular frequency shape 264\u003c\/p\u003e \u003cp\u003e9.3.2.2. Circular shape 266\u003c\/p\u003e \u003cp\u003e9.3.3. Digital 2-D filter design by windowing 271\u003c\/p\u003e \u003cp\u003e9.3.4. Applying filters based on rectangular and circular shapes 271\u003c\/p\u003e \u003cp\u003e9.3.5. 2-D Gaussian filters 274\u003c\/p\u003e \u003cp\u003e9.3.6. 1-D and 2-D representations in a continuous space 274\u003c\/p\u003e \u003cp\u003e9.3.6.1. 2-D specifications 276\u003c\/p\u003e \u003cp\u003e9.3.7. Approximation for FIR filters 277\u003c\/p\u003e \u003cp\u003e9.3.7.1. Truncation of the Gaussian profile 277\u003c\/p\u003e \u003cp\u003e9.3.7.2. Rectangular windows and convolution 279\u003c\/p\u003e \u003cp\u003e9.3.8. An example based on exploiting a modulated Gaussian filter 280\u003c\/p\u003e \u003cp\u003e9.4. Appendix: spatial window functions and their implementation 286\u003c\/p\u003e \u003cp\u003e9.5. Bibliography 291\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 10. Filter Stability 293\u003c\/b\u003e\u003cbr\u003e \u003ci\u003eMichel BARRET\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e10.1. Introduction 293\u003c\/p\u003e \u003cp\u003e10.2. The Schur-Cohn criterion 298\u003c\/p\u003e \u003cp\u003e10.3. Appendix: resultant of two polynomials 314\u003c\/p\u003e \u003cp\u003e10.4. Bibliography 319\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 11. The Two-Dimensional Domain 321\u003c\/b\u003e\u003cbr\u003e \u003ci\u003eMichel BARRET\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e11.1. Recursive filters 321\u003c\/p\u003e \u003cp\u003e11.1.1. Transfer functions 321\u003c\/p\u003e \u003cp\u003e11.1.2. The 2-D z-transform 322\u003c\/p\u003e \u003cp\u003e11.1.3. Stability, causality and semi-causality 324\u003c\/p\u003e \u003cp\u003e11.2. Stability criteria 328\u003c\/p\u003e \u003cp\u003e11.2.1. Causal filters 329\u003c\/p\u003e \u003cp\u003e11.2.2. Semi-causal filters 332\u003c\/p\u003e \u003cp\u003e11.3. Algorithms used in stability tests 334\u003c\/p\u003e \u003cp\u003e11.3.1. The jury Table 334\u003c\/p\u003e \u003cp\u003e11.3.2. Algorithms based on calculating the Bezout resultant 339\u003c\/p\u003e \u003cp\u003e11.3.2.1. First algorithm 340\u003c\/p\u003e \u003cp\u003e11.3.2.2. Second algorithm 343\u003c\/p\u003e \u003cp\u003e11.3.3. Algorithms and rounding-off errors 347\u003c\/p\u003e \u003cp\u003e11.4. Linear predictive coding 351\u003c\/p\u003e \u003cp\u003e11.5. Appendix A: demonstration of the Schur-Cohn criterion 355\u003c\/p\u003e \u003cp\u003e11.6. Appendix B: optimum 2-D stability criteria 358\u003c\/p\u003e \u003cp\u003e11.7. Bibliography 362\u003c\/p\u003e \u003cp\u003e\u003ci\u003eList of Authors 365\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e\u003ci\u003eIndex 367\u003c\/i\u003e\u003c\/p\u003e \u003cb\u003eMohamed Najim\u003c\/b\u003e has published several books, more than 220 technical papers and has taught courses in digital signal processing for more than 30 years.  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.\u003cbr\u003e 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.","brand":"Wiley-ISTE","offers":[{"title":"Default Title","offer_id":47989065220325,"sku":"NP9781905209453","price":316.95,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781905209453.jpg?v=1761782650","url":"https:\/\/k12savings.com\/es\/products\/digital-filters-design-for-signal-and-image-processing-isbn-9781905209453","provider":"K12savings","version":"1.0","type":"link"}