Digital Filter Designer's Handbook: Featuring C Routines

Description

This hands-on guide for circuit designers, technicians, and students discusses digital filter specification and design techniques. The book's coverage begins with a review of filter design fundamentals, complete with all the necessary mathematical background, and proceeds through the theory, operation, design and implementation of every available type of digital filter. The book compiles practical information from many diverse, technical sources and translates it into plain English. It is extensively cross-referenced and breaks down complicated procedures with step-by-step algorithms. It includes application examples and is accompanied by a disk of design programmes written in the C language. Digital Filter Designer's Handbook Contents List of Programs Preface Ch1 Mathematical Review 1.1 Exponentials & Logarithms Exponentials Logarithms Decibels 1.2 Complex Numbers Operations on complex numbers in rectangular form Polar form of complex numbers Consider three complex numbers: Multiplication Division Powers Roots Logarithms of complex numbers 1.3 Trigonometry Phase shifting of sinusoids Trigonometric identities Euler's identities Series & product expansions Orthonormality of sine & cosine 1.4 Derivatives Derivatives of polynomial ratios 1.5 Integration 1.6 Dirac Delta Function Distributions Properties of delta distribution 1.7 Mathematical Modeling of Signals Steady-state signal models Periodicity Symmetry Energy Signals versus Power Signals 1.8 Fourier Series Trigonometric Forms Exponential Form Conditions of Applicability Properties of Fourier Series 1.9 Fourier Transform Fourier Transforms of Periodic Signals Common Fourier Transform Pairs 1.10 Spectral Density Energy Spectral Density Power Spectral Density of Periodic Signal Ch2 Filter Fundamentals 2.1 Systems Linearity Time Invariance Causality 2.2 Characterization of Linear Systems Impulse Response Step Response 2.3 Laplace Transform Background 2.4 Properties of Laplace Transform Time Shifting Multiplication 2.5 Transfer Functions 2.6 Heaviside Expansion Simple Pole Case 2.7 Poles & Zeros 2.8 Magnitude, Phase & Delay Responses Phase Delay Group Delay 2.9 Filter Fundamentals Magnitude Response Features of Lowpass Filters Scaling of Lowpass Filter Responses Magnitude Scaling. Phase Response. Step Response. Impulse Response. Highpass Filters Bandpass Filters Wide-Band Bandpass Filters Narrow-Band Bandpass Filters Listing 2.1 laguerreMethod( ) Listing 2.2 unwrapPhase( ) Ch3 Butterworth Filters 3.1 Transfer Function 3.2 Frequency Response 3.3 Determination of Minimum Order for Butterworth Filters 3.4 Impulse Response of Butterworth Filters 3.5 Step Response of Butterworth Filters Listing 3.1 butterworthFreqResponse( ) Listing 3.2 butterworthImpulseResponse() Ch4 Chebyshev Filters 4.1 Transfer Function 4.2 Frequency Response 4.3 Impulse Response 4.4 Step Response Listing 4.1 chebyshevFreqResponse( ) Listing 4.2 chebyshevirnpulseResponse( Ch5 Elliptical Filters 5.1 Parameter Specification 5.2 Normalized-Transfer Function 5.3 Denormalized-Transfer Function Listing 5.1 cauerOrderEstim( ) Listing 5.2 cauerCoeffe() Listing 5.3 cauerFreqResponse() Listing 5.4 cauerRescale() Ch6 Bessel Filters 6.1 Transfer Function 6.2 Frequency Response 6.3 Group Delay Listing 6.1 besselCoefficients() Listing 6.2 besselFreqResponse() Listing 6.3 besselGroupDelay() Ch7 FundamentaIs of DigitaI Signal Processing 7.1 Digitization Ideal Sampling Instantaneous Sampling Natural Sampling Discrete-Time Signals Notation 7.2 Discrete-Time Fourier Transform Discrete-Time Fourier Transform Convergence Conditions Relationship to Fourier Series 7.3 Discrete-Time Systems Difference Equations Discrete Convolution 7.4 Diagramming Discrete-Time Systems Block Diagrams Multiplier Summer Signal Flow Graphs Ch8 Discrete Fourier Transform 8.1 Discrete Fourier Transform Parameter Selection Periodicity 8.2 Properties of DFT Linearity Symmetry Time Shifting Frequency Shifting Even & Odd Symmetry Real & Imaginary Properties 8.3 Implementing DFT 8.4 Fast Fourier Transforms 8.5 Applying Discrete Fourier Transform Short Time-Limited Signals Periodic Signals Long Aperiodic Signals Listing 8.1 dft() Listing 8.2 dft2() Listing 8.3 fft() Ch9 z Transform 9.1 Region of Convergence Finite-Duration Sequences Infinite-Duration Sequences Convergence of Unilateral z Transform 9.2 Relationship between Laplace & z Transforms 9.3 System Functions 9.4 Common z-Transform Pairs & Properties 9.5 Inverse z Transform 9.6 Inverse z Transform via Partial Fraction Expansion Ch10 FIR Filter Fundamentals 10.1 Introduction to FIR Filters FIR Advantages FIR Disadvantages 10.2 Evaluating Frequency Response of FIR Filters 10.3 Linear Phase FIR Filters Listing 10.1 cgdFirResponse() Listing 10.2 normalizeResponse() Ch11 Fourier Series Method of FIR Filter Design 11.1 Basis of Fourier Series Method Properties of Fourler Series Method 11.2 Rectangular Window Discrete-Time Window Frequency Windows & Spectral Windows 11.3 Triangular Window Discrete-Time Triangular Window 11.4 Window Software 11.5 Applying Windows to Fourier Series Filters 11.6 von Hann Window Discrete-Time von Hann window 11.7 Hamming Window Discrete-Time Hamming Windows Computer Generation of Window Coefficients 11.8 Dolph-Chebyshev Window Listing 11.1 idealLowpass() Listing 11.2 idealResponse() Listing 11.3 idealBandpass() Listing 11.4 idealBandstop() Listing 11.5 contRectangolarResponse() Listing 11.6 discRectangularResponse() Listing 11.7 contTriangularResponse() Listing 11.8 discTrianguiarResponse() Listing 11.9 triangularWindow() Listlng 11.10 makeLagWindow() Listing 11.11 makeDataWindow() Listing 11.12 hannWindow() Listing 11.13 hammingWindow() Ch12 FIR Filter Design: Frequency Sampling Method 12.1 Introduction 12.2 Odd N versus Even N Even N 12.3 Design Formulas 12.4 Frequency Sampling Design with Transition-Band Samples Optimization 12.5 Optimization with Two Transition-Band Samples Programming Considerations 12.6 Optimization with Three Transition-Band Samples Listing 12.1 fsDesign() Listing 12.2 findSbPeak() Listing 12.3 goldenSearch(0 Listing 12.4 setTrans() Listing 12.5 goldenSearch2() Listing 12.6 setTransition() Listing 12.7 optimize2() Listing 12.8 dumpRectComps() Ch13 FIR Filter Design: Remez Exchange Method 13.1 Chebyshev Approximation Alternation Theorem 13.2 Strategy of Remez Exchange Method 13.4 Selecting Candidate Extremal Frequencies Testing E(f) for f=0 Testing E(f) within Pass Band & Stop Band Testing of E(f) at Pass-Band & Stop-Band Edges Testing of E(f) for f=0.5 Rejecting Superfluous Candidate Frequencies Deciding When to Stop 13.5 Obtaining Impulse Response 13.6 Using Remez Exchange Method Deciding on Filter Length 13.7 Extension of Basic Method Listing 13.1 gridFreq() Listing 13.2 desLpfResp() Listing 13.3 weightLp() Listing 13.4 remezError() Listing 13.5 computeRemezA() Listing 13.6 remezSearch() Listing 13.7 remezStop( ) Listing 13.8 remezStop2() Listing 13.9 remezFinish() Listing 13.10 remez() Ch14 IIR Filters 14.1 Frequency Response of IIR Filters 14.2 IIR Realizations 14.3 Impulse lnvariance Programming Considerations 14.4 Step lnvariance Programming Considerations Listing 14.1 iirResponse( ) Listing 14.2 impulseInvar() Listing 14.3 stepInvar() Ch15 IIR Filters via Bilinear Transformation 15.1 Bilinear Transformation 15.2 Factored Form of Bilinear Transformation 15.3 Properties of Bilinear Transformation Frequency Warping 15.4 Programming Bilinear Transformatlon Listing 15.1 bilinear() Ch16 Practical Considerations 16.1 Binary Representation of Numeric Values Fixed-Point Formats Floating-Point Formats 16.2 Quantized Coefficients 16.3 Quantization Noise AppA GlobaI Definitions AppB Prototypes for C Functions AppC Functions for Complex Arithmetic AppD Miscellaneous Support Functions Bibliography Index p250-251 Missing