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Digital Filter. Designer's Handbook. Featuring C Routines. C. Britton Rorabaugh. TAB BOOKS. Division of McGraw-Hill, Inc. Blue Ridge Summit,PA 17294-0850
viii Contents 3.4 Impulse Response of Butterworth FIlters 3.5 Step Response of Butterwoth Filters Chapter 4. Chebyshev Filters 4.1 Transfer Function 78 4.2 Frequency Response 4. 3 Impulse Response 4.4 Step Response Chapter 5. Elliptical Filters 93 5.1 Parameter Specification 5.2 Normalized-Transfer Function 5.3 Denormalized-Transfer Function Chapter 6. Bessel Filters 6 Transfer Function 6.2 Frequency Response 111 6.3 Group Delay 111 Chapter 7. Fundamentals of Digital Signal Processing 7.1 Digitization 117 7.2 Discrete-Time Fourier Transform 127 73 Discrete-TIme Systems 129 7.4 Diagramming Discrete-Time Systems 131 Chapter 8. Discrete Fourier Transform 137 8.1 Discrete Fourier Transfor 137 8.2 Properties of the DFT 8.3 Implementing the DFT 141 8. 4 Fast Fourier Transforms 141 8.5 Applying the Discrete Fourier Transform 143 Chapter 9. The z Transform 151 9.1 Region of Convergence 9.2 Relationship between the Laplace and z Transforms 155 9. 3 System Functions 9.4 Common z-Transform Pairs and Properties 15G 9.5 Inverse z Transform 157 9.6 Inverse z Transform via Partial Fraction Expansion 157 Contents ix Chapter 10. FIR Filter Fundamentals 161 10.1 Introductlon to FIR Filters 161 10.2 Evaluating the Frequency Response of FiR Filters 162 10.3 Linear Phase FIR FIlters 163 Chapter 11. Fourier Series Method of FIR Filter Design 171 11.1 BasIs of the Fourler Series Method 171 11.2 Rectangular Window 179 113了 riangular WIndow 11.4 Window Software 11.5 Applying Windows to Fourler Serles FIlters 11. 6 von Hann WIndo 193 11.7 Hamming Window 197 11.8 Dolph-Chebyshev Window 199 Chapter 12. FIR Fllter Design: Frequency Sampling Method 211 12.1 Introduction 211 12.2 Odd N versus Even N 214 12.3 Design Formulas 218 12.4 Frequency Sampling Design with Transition-Band Samples 219 12.5 Optimization with Two Transitlon-Band Samples 223 12.6 Optimization with Three Transitlon-Band Samples Chapter 13. FIR Filter Design: Remez Exchange Method 245 13.1 Chebshev Approximation 246 13.2 Strategy of the Remez Exchange Method 13.3 Evaluating the Error 13.4 Selecting Candidate Extremal Frequencies 252 13.5 Obtaining the Impulse Response 255 13.6 Using the Remez Exchange Method 255 13.7 Extension of the Basic Method 259 Chapter 14. HIR Filters 14.1 Frequency Response of IIR Filters 272 14.2 R Realizations 272 14.3 Impulse Invariance 274 14.4 Step Invariance 279 Chapter 15. IIR Filters via the BIlinear Transformation 287 15.1 BIlinear Transformation 287 15.2 Factored Form of the BIflnear Transformation 288 15. 3 Properties of the Bilinear Transformation 15.4 Programming the Bilinear Transformation 29 Contents Chapter 16. Practical Considerations 16.1 Binary Representation of Numeric Values 299 16.2 Quantized Coefficient 16.3 Quantization Noise Appendix A. Global Definitions 31t Appendix B. Prototypes for C Functions 313 Appendix C. Functions for Complex ArithmetIc 321 Appendix D. Miscellaneous Support Functions 325 Bibliography 329 Index 331 List of Programs Listing 2.1 laguerreMethod( 62 Listing 2.2 unwrapPhase() 64 Listing 3.1 butterworth FreqResponse) 74 Listing 3.2 butterworthlmpulseResponse() Listing 4.t chebyshevFreqResponse( Listing 4.2 chebyshevImpulseResponse( Listing 5.1 cauerOrderEstim( 102 Listing 5.2 auerCoeffs() 103 Listing 5.3 cauerFreq() 105 Listing 5. 4 cauerRescale() 106 Listing 6.1 besselCoefflcients() 113 Listing 6.2 besselFreq Response() 114 Listing 6.3 besselGroupDelay( 115 Listing 8.1 dA() 147 Listing 8.2 dft2() 147 Listing 8.3 fit) 148 Listing 10.1 cgdFirResponse() 167 Listing 10.2 normalizeResponse() 16 Listing 11.1 idealLowpass() 201 xl LIst of Programs Listing 11.2 idealHighpass( 201 Listing 11.3 idealBandpass() 202 Listing 11.4 idealBandstoP() 243 Listing 11.5 contRectangularResponse() 203 Listing 11.6 discRectangularResponse) 204 Listing 11.7 contTrlangularResponse() 205 LIsting 11.8 discTriangularResponse() 205 Listing 11. 9 triangularWindow() 206 Listing 11.10 makeLagwindow( y 206 Listing 11.11 make Datawindow() 207 Listing 11.12 hannWindow() 208 Listing 11.13 hamming Window() Listing 12.1 fsDeslgn() 231 Listing 12.2 findsbPeak( 233 Listing 12. 3 golden Search( Listing 12.4 setTrans( 237 Listing 12.5 golden Search2() 238 LIsting 12.6 setTransition() 240 Listing 12.7 optimize( 242 Listing 12.8 dumpRectcomps() 243 Listing 13.1 gridFreq( Listing 13.2 desLpfResP() 262 Listing 13.3 weightLp() 262 LIsting 13.4 remezError( 263 LIsting 13.5 computeRemezA() 253 Listing 13.6 remezSearch() 265 Listing 13.7 remezStop() 267 List of Programs xili LIsting 13. 8 remezStop2() 268 Listing 13.9 remezFinish( 268 Listing 13.10 remez) 269 Listing 14.1 iirResponse() 282 LIstIng 14.2 impulselnvar( 283 Listing 14.3 steplnvar() Listing 15.1 bilinear( Appendix A Global Definitions 311 Appendix B Prototypes for C Functions AppendIx c Functions for Complex Arithmetic 321 Appendix D MIscellaneous Support Functions 325 Preface If you're going to own only one book on digital filters, this is the one to have. If you already own several, you need this book anyway--it contains quite a lot of useful information not available in any other book. I wrote this book for individuals faced with the need to design working digital filters--it is not intended as an academic text. All the necessary theoretical background is provided in the early chapters, and practical digital filter design techniques are provided in the later chapters. These design techniques are supported by numerous com puter routines written in the C programming language. The tech- niques and programs presented in this book will prove to be very useful to engineers, students, and hobbyists engaged in the design of digital filters All of the programs in this book were written and tested using Think C for the Apple macintosh computer. I made a conscientious effort to limit the programs to the ansi standard subset of Think C and to avoid any machine dependencies. Potential efficiencies were sacrificed for the sake of portability and tutorial clarity. However, a few specific items need to be pointed out: Constants used by several different functions are collected into a single include"file called globDefs h(a listing of this file is provided in App. A). The"new"style of ANSI prototyping was used throughout all of the software generated for this book. All the pertinent prototypes are collected in a file called protos.h, which is provided in App. B 2. Nice long file names such as computeRemezAmplitude c are allowed on the macintosh, but on MS-Dos machines fle names are limited to eight characters plus a three-character extension. Except for the two header files mentioned above, all the files on the accompa- nying disk have names that are keyed to the chapter number in which the listing appears xvi Preface 3. I found it convenient to define a new type real that is the same as double. For use on machines with limited memory, real could be redefined as float to save memory, but accuracy could suffer being a long-time Fortran user, I also found it convenient to create a logical type. The lack of intrinsic complex types in C was overcome via a complex structure definition, and a set of complex arithmetic func tions is detailed in App. C. Britt rorabaugh

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