Digital Signal Processing
Subtitle: Principles, Algorithms, and Applications
Publisher: PRENTICE-HALL INTERNATIONAL, INC.
Published: April 7, 2006
Language: eng
ISBN-13: 9780131873742
Table of contents: title: PREFACE; title: 1  INTRODUCTION; title: 1.1  Signals, Systems. and Signal Processing  2; title: 1.1.1  Basic Elements of  a  D~gital Signal Processing System. 4; title: 1.1.2  Advantages of  Digital over  Analog Signal Processing, 5; title: 1.2  Classification of  Signals  6; title: 1.2.1  Multichannel  and  Multidimensional  Signals. 7; title: 1.2.2  Continuous-Time Versus Discrete-Tlme Signals. 8; title: 1.2.3  Continuous-Valued Versus Discrete-Valued Signals. 10; title: 1.2.4  Determinist~c Versus  Random Signals. 11; title: 1.3  The  Concept of  Frequency  in  Continuous-Time  and; title: Discrete-Time Signals  14; title: 1.3.1  Continuous-Time Sinusoidal Signals, 14; title: 1.3.2  Discrete-Time Sinusoidal Signals. 16; title: 1.3.3  Harmonically  Related Complex  Exponentials, 19; title: 1.4  Analog-to-Digital and Digital-to-Analog Conversion  21; title: 1.4.1  Sampling of  Analog Signals, 23; title: 1.4.2  The Sampling Theorem, 29; title: 1.4.3  Quantization of Continuous-Amplitude Signals, 33; title: 1.4.4  Quantization of Sinusoidal Signals. 36; title: 1.4.5  Coding of  Quantized Samples. 38; title: 1.4.6  Digital-to-Analog Conversion, 38; title: 1.4.7  Analysis  of  Digital Signals and  Systems  Versus Discrete-Time; title: Signals and Systems, 39; title: 1.5  Summary and  References  39; title: Problems  40 2  DISCRETE-TIME SIGNALS AND SYSTEMS; title: Contents; title: 43; title: 2.1  Discrete-Time  Signals  43; title: 2.1.1  Some Elementary  Discrete-Time Signals, 45; title: 2.1.2  Classification of  Discrete-Time Signals, 47; title: 2.1.3  Simple  Manipulations  of  Discrete-Time Signals, 52; title: 2.2  Discrete-Time Systems  56; title: 2.2.1  Input-Output Description of  Systems. 56; title: 2.2.2  Block Diagram Representation of Discrete-Time Systems, 59; title: 2.2.3  Classification of  Discrete-Time Systems, 62; title: 2.2.4  Interconnection of  Discrete-Time Systems, 70; title: 2.3  Analysis of  Discrete-Time  Linear Time-Invariant Systems  72; title: 2.3,1  Techniques for the Analysis of  Linear Systems, 72; title: 2.3.2  Resolution of  a Discrete-Time Signal into Impulses, 74; title: 2.3.3  Response of  LTI Systems  to Arbitrary Inputs:  The  Convolution; title: Sum, 75; title: 2.3.4  Properties of  Convolution  and  the  Interconnection  of  LTI; title: Systems, 82; title: 2.3.5  Causal  Linear Time-Invariant  Systems. 86; title: 2.3.6  Stability of  Linear Time-Invariant Systems, 87; title: 2.3,7  Systems with  Finlte-Duration  and  infinite-Duration  Impulse; title: Response. 90; title: 2.4  Discrete-Time Systems Described  by  Difference Equations  91; title: 2.4.1  Recursive and  Nonrecursive Discrete-Time  Systems. 92; title: 2.4.2  Linear  Time-Invariant  Systems  Characterized  by; title: Constant-Coefficient  Difference Equations. 95; title: 2.4.3  Soiution of  Linear Constant-Coefficient Difference Equations. 100; title: 2.4.4  The  Impulse  Response of  a  Linear Tirne-Invariant  Recursive; title: System. 108; title: 2.5  Implementation  of  Discrete-Time  Systems  111; title: 2.5.1  Structures for  the  Realization  of  Linear  Time-Invariant; title: Systems. 111; title: 2.5.2  Recursive  and  Nonrecursive ReaIizations of  FIR Systems. 116; title: 2.6  Correlation  of  Discrete-Time  Signals  118; title: 2.6.1  Crosscorrelation  and Autocorrelation  Sequences. 120; title: 2.6.2  Properties  of  the Autocorrelation  and  Crosscorrelation; title: Sequences. 122; title: 2.6.3  Correlation of  Periodic Sequences. 124; title: 2.6.4  Computation of  Correlation  Sequences. 130; title: 2.6.5  Input-Output  Correlation  Sequences. 131; title: 2.7  Summary and References  134; title: Problems  135 Contents  v; title: 3  THE I-TRANSFORM AND ITS APPLICATION TO THE ANALYSS; title: OF LTI SYSTEMS  151; title: 3.1  The :-Transform  151; title: 3.1.1  The Direct  :-Transform.  152; title: 3.1.2  The Inverse  :-Transform.  160; title: 3.2  Properties of  the ;-Transform  161; title: 3.3  Rational :-Transforms  172; title: 3.3.1  Poles and Zeros. 172; title: 3,3.2  Pole  Location and Time-Domain  Behavior  for Causal Signals. 178; title: 3.3.3  The System Function of  a Linear Time-Invariant  System.  181; title: 3.4  Inversion of  the :-Transform  184; title: 3.4.1  The Inverse :-Transform  by  Contour  Integration.  184; title: 3,4.2  The Inverse :-Transform  hg Power Serles Expansion.  186; title: 3.4.3  The Inverse  :-Transform  by  Partial-Fraction  Expansion.  188; title: 3.4.4  Decomposition of  Rational  :-Transforms.  195; title: 3.5  The One-sided  :-Transform  197; title: 3.5.1  Definit~on and  Properties. 197; title: y.52  Solution  of  Difference  Equations. 201; title: 3.6  Analysis of  Linear Time-Invariant Systems  in  the :-Domain  303; title: -3.6.1  Response ol Systems with  Rational System  Functions. 203; title: 3,6.2  Response  of  Pole-Zero  Systems  with  Nonzero  Initial; title: Condi~ions. 204; title: 3.6.3  Transient  and Steady-State  Responses, 206; title: 3.6.4  Causalit!,  and Stability. 208; title: 3.6.5  Pole-Zero  Cancellations. 210; title: 3.6.6  Multiple-Order Poles and  Stabihty. 211; title: 3.6.7  The Schur-Cohn Stability Test. 213; title: 3.6.8  Stability  of  Second-Order  Systems. 215; title: 3.7  Summary and  References  219; title: Problems  220; title: 4  FREQUENCY ANALYSIS OF SIGNALS AND SYSTEMS; title: 4.1  Frequency Analysis of  Continuous-Time Signals  230; title: 4.1.1  The Fourier Series for Continuous-Time Periodic Signals. 232; title: 4.1.2  Power Density Spectrum of  Periodic  Signals. 235; title: 4.1.3  The  Fourier Transform  for  Continuous-Time  Aperiodic; title: Signals. 240; title: 4.1.4  Energy Density  Spectrum of  Aperiodic Signals. 243; title: 4.2  Frequency Analysis of  Discrete-Time Signals  247; title: 4.2.1  The Fourier Series for Discrete-Time Periodic Signals. 247 Contents; title: 4.2.2  Power  Density  Spectrum of  Periodic Signals. 250; title: 4.2.3  The Fourier Transform of  Discrete-Time  Aperiodic Signals. 253; title: 4.2.4  Convergence of the Fourier Transform, 256; title: 4.2.5  Energy Density Spectrum of  Aperiodic Signals, 260; title: 4.2.6  Relationship of the  Fourier Transform  to the z-Transform, 264; title: 4.2.7  The Cepstrum, 265; title: 4.2.8  The Fourier  Transform  of  Signals with Poles on  the  Unit; title: Circle. 267; title: 4.2.9  The Sampling Theorem  Revisited, 269; title: 4.2.10  Frequency-Domain Classification  of  Signals:  The Concept of; title: Bandwidth, 279; title: 4.2.11  The Frequency  Ranges of  Some Natural Signals. 282; title: 4.2.12  Physical and  MathematicaI  Dualities.  282; title: 4.3  Properties  of  the  Fourier  Transform  for  Discrete-Time; title: Signals  286; title: 4.3.1  Symmetry  Properlies of  the Fourier Transform, 287; title: 4.3.2  Fourier Transform  Theorems  and  Properties. 294; title: 4.4  Frequency-Domain  Characteristics of  Linear Time-Invariant; title: Systems  305; title: 4.4.1  Response to Complex  Exponential  and Sinusoidal  Signals:  The; title: Frequency  Response Function. 3%; title: 4.4.2  Steady-State  and  Transient  Response  to Sinusaidal  Input; title: Signals. 314; title: 4.4.3  Steady-State Response to  Periodic Input Signals, 315; title: 4.4.4  Response  lo Aperiodic Input Signals. 316; title: 4.4.5  Relationships Between  the System  Function  and  the Frequency; title: Response Function. 319; title: 4.4.6  Computation  of  the Frequency Response  Function. 321; title: 4.4.7  Input-Output Correlation  Functions and Spectra. 325; title: 4.4.8  Correlation  Functions and  Power  Spectra  for  Random  Input; title: Signals. 327; title: 4.5  Linear Time-Invariant  Systems  as Frequency-Selective; title: Filters  330; title: 4.5.1  Ideal Filter Characteristics. 331; title: 4.5.2  Lowpass, Highpass, and  Bandpass filters. 333; title: 4.5.3  Digital  Resonators. 340; title: 4.5.4  Notch Filters.  343; title: 4.5.5  Comb Filters, 345; title: 4.5.6  All-Pass Fihers. 350; title: 4.5.7  Digital Sinusoidal  Oscil~ators. 352; title: 4.6  Inverse Systems and Deconvolution  355; title: 4.6.1  Invertibility  of  Linear T~me-Invariant Systems. 356; title: 4.6.2  Minimum-Phase.  Maximum-Phase, and  Mixed-Phase Systems. 359; title: 4.6.3  System  Identification  and  Deconvolution, 363; title: 4.6.4  Homomorphic  Deconvo~ution. 365 Contents; title: 4.7  Summary and  References  367; title: Problems  368; title: 5  THE DISCRETE  FOURIER TRANSFORM: ITS PROPERTIES  AND; title: A PPLICATIONS  394; title: 5.1  Frequency  Domain  Sampling:  The  Discrete  Fourier; title: Transform  394; title: 5.1.1  Frequency-Domain  Sampling  and  Reconstruction  of; title: Discrete-Time Signals. 394; title: 5.1.2  The  Discrete Fourier  Transform  (DFT). 399; title: 5.1.3  The DFT as a Linear Transformation. 403; title: 5.1.4  Relationship of the  DFT to Other Transforms, 407; title: 5.2  Properties of  the D l T   409; title: 5.2.1  Periodicity.  Linearity. and  Symmetry  Properties. 410; title: 5.2.2  Multiplication  of Two DFTs and  Circular Convolution. 415; title: 5.2.3  Additional  DFT Properties. 421; title: 5.3  Linear Filtering Methods Based on  the DFT  425; title: 5.3.1  Use of  thc  DFT in  Linear Filtering. 426; title: 5.3.2  Filtering of  Long Data Sequences.  430; title: 5.4  Frequency Analysis of  Signals Using the DFT  433; title: 5.5  Summary  and  References  440; title: Problems  440; title: 6  EFFICIENT  COMPUTATION OF THE  DFT: FAST  FOURIER; title: TRANSFORM ALGORITHMS  448; title: 6.1  Efficient Computation  of  the  DFT FFT Algorithms  448; title: 6.1.1  Direct Computation  of  the  DFT. 449; title: 6.1.2  Divide-and-Conquer  Approach  to Computation  of  the DFT. 450; title: 6.1.3  Radix-2  FFT Algorithms.  456; title: 6.1.4  Radix-4  FFT Algorithms. 465; title: 6.1.5  Split-Radix FFT Algorithms, 470; title: 6.1.6  Implementation  of  FFT Algorithms.  473; title: 6.2  Applications of  FFT Algorithms  475; title: 6.2.1  Efficient Computation  of  the DFT of  Two  Real Sequences. 475; title: 6.2.2  Efficient  Computation  of  the  DFT of  a  2N-Point  ReaI; title: Sequence, 476; title: 6.2.3  Use of  the FFT Algorithm in  Linear Filtering and Correlation. 477; title: 6.3  A  Linear Filtering Approach  to Computation  of  the D l T   479; title: 6.3.1  The  Goertzel Algorithm, 480; title: 6.3.2  The Chirp-z Transform Algorithm, 482 viii  Contents; title: 6.4  Quantization  Effects in  the  Compuration  of  the  DFT  486; title: 6.4.1  Quantization  Errors in  the Direct  Computation  of  the DFT. 487; title: 6.4.2  Quantization  Errors in  FFT Algorithms. 489; title: 6.5  Summary and  References  493; title: Problems  494; title: 7  IMPLEMENTATION OF DISCRETE- TIME SYSTEMS; title: 7.1  Structures for the Realization of  Discrete-Time Systems  500; title: 7.2  Structures for FIR Svstems  502; title: 7.2.1  Direcl-Form Structure. SO3; title: 7.2.2  Cascade-Form Structures. 504; title: 7.2.3  Frequency-Sampling  Structurest. 506; title: 7.2.4  Lattice Structure. 511; title: 7.3  Structures for  IIR Systems  519; title: 7.3.1  Direct-Form  Structures. 519; title: 7.3.3  Signal  Flow  Graphs and Transposed  Structures. 521; title: 7.3.3  Cascade-Form Strucrures. 526; title: 7.3.4  Parallel-Form  Structures. 529; title: 7.3.5  Latticc and  Lattice-Ladder  Structures  for  IIR  Syslcms. 531; title: 7.4  State-Space System Analvsis and Structures  5.19; title: 7.4.1  State-Space Descriptions of  Svstems  Characlerizcd  h!  Diflerencc; title: Equations. 540; title: 7.4.2  Solution  of  the State-Space  Equations. 543; title: 7.4.3  Relationships  Between  Input-Outpur  and State-Space; title: Descriptions.  545; title: 7.4.4  State-Space Analysis in  the z-Domain. 550; title: 7.4.5  Additional State-Space Structures. 554; title: 7.5  Representation  of  Numbers  556; title: 7.5.1  Fixed-Poinr  Representation  of  Numbers. 557; title: 7.5.2  Binary  Floating-Point  Representation of  Numbers.  561; title: 7.5.3  Errors Resulting from  Rounding and  Truncation. 56d; title: 7.6  Quantization  of  Filter Coefficients  569; title: 7.6.1  Analysis of  Sensitivity to Quantization  of  Filter  Coefficients. 569; title: 7.6.2  Quantization  of  Coefficients in FIR  Filters. 578; title: 7.7  Round-Off  Effects in  Digital Filters  582; title: 7.7.1  Limit-Cycle Oscillations  in Recursive Systems. 583; title: 7.7.2  Scaling  to Prevent Overflow. 588; title: 7.7.3  Statistical  Characterizatton of  Quantization  Effects  in  Fixed-Point; title: Realizations  of  Digital Filters.  590; title: 7.8  Summary  and  References  598; title: Problems  600 Contents; title: 8  DESIGN OF DIGITAL FILTERS; title: 8.1  General Considerations  614; title: 8.1.1  Causality  and  Its Implications. 615; title: 8.1.2  Characteristics of  Practical  Frequency-Selective  Filters. 619; title: 8.2  Design of  FIR Filters  620; title: 8.2.1  Symmetric and Antisymmerrir FIR Filters. 620; title: 8.2.2  Design  of  Linear-Phase  FIR Filters Using Windows. 623; title: 8.2,3  Design  of  Llnear-Phase FIR Filters by  the  Frequency-Sampling; title: Method. 630; title: 8.2.4  Design  of  Optimum  Equiripple Linear-Phase  FIR Filters, 637; title: 8.2.5  Design  of  FIR Differentiators. 652; title: 8.2.6  Design  of  Hilbert Transformers, 657; title: 8.2.7  Comparison of  Design  Methods for Linear-Phase  FIR Filters. 662; title: 8.3  Design of  IIR Filters  From  Analog Filters  666; title: 8.3.1  IIR Filter Design  by  Approximation of  Derivatives. 667; title: 8.3.2  11R Filter Design  by Impulse  Invariance. 671; title: 8.3.3  IIR Filter Design  by  the Bilinear  Transformation.  676; title: 8.3,4  The Matched-:  Transformation,  681; title: 8.3.5  characteristics of  Commonly  Used  Analog Filters. 681; title: 8.3.6  Same Examples of  Digital  Filter Designs Based  on  the Bilinear; title: Transformation. 692; title: 8.4  Frequency Transformations  692; title: 8.4.1  Frequency Transformations  in  the Analog Domain. 693; title: 8.4.2  Frequency Transformations  in  the Digital  Domain. 698; title: 8.5  Design of  Digital Filters  Based  on  Least-Squares  Method  701; title: 8.5.1  Pade Approximation  Method. 701; title: 8.5.2  Least-Squares Design  Methods. 706; title: 8.5.3  FIR Least-Squares Inverse  (Wiener) Filters, 711; title: 8 5 4   Design  of  IIR Filters in the Frequency Domain, 719; title: 8.6  Summary and  References  724; title: Problems  726; title: 9  SAMPLING  AND RECONSTRUCTION OF SIGNALS; title: 9.1  Sampling of  Bandpass Signals  738; title: 9.1.1  Representation  of  Bandpass Signals. 738; title: 9.1.2  Sampling of  Bandpass Signals, 742; title: 9.1.3  Discrete-Time Processing of  Continuous-Time Signals. 746; title: 9.2  Analog-to-Digital Conversion  748; title: 9.2.1  Sample-and-Hold. 748; title: 9.2.2  Quantization  and Coding, 750; title: 9.2.3  Analysis of  Quantization  Errors, 753; title: 9.2.4  Oversampling A/D Converters, 756 Contents; title: 9.3  Digital-to-Analog Conversion  763; title: 9.3.1  Sample and  Hold. 765; title: 9.3.2  First-Order  Hold. 768; title: 9.3.3  Linear  Interpolation  with Delay.  771; title: 9.3.4  Oversampling DIA Converters, 774; title: 9.4  Summary  and  References  774; title: Problems  775; title: 10  MULTIRATE DIGITAL SIGNAL PROCESSING; title: 10.1  Introduction  783; title: 10.2  Decimation  by  a Factor D  784; title: 10.3  Interpolation  by  a Factor I  787; title: 10.4  Sampling  Rate Conversion  by  a Rational  Factor  IID  790; title: 10.5  Filter  Design  and  Implementation  for  Sampling-Rate; title: Conversion  792; title: 10.5.1  Direct-Form FIR  Filter Structures, 793; title: 10.5.2  Polyphase  Filter Structures. 794; title: 10.5.3  Time-Variant  Filter Structures. 800; title: 10.6  Multistage  Implementation  oi Sampling-Rate  Conversion  806; title: 10.7  Sampling-Rate Conversion  of  Bandpass Signals  810; title: 10.7.1  Decimation and Interpolation  by Frequency Conversion. 812; title: 10.7.2  Modulation-Free  Method  for Decimation  and Interpolation. 814; title: 10.8  Sampling-Rate Conversion  by  an Arbitrary  Factor  815; title: 10.8.1  First-Order  Approximation. 816; title: 10.8.2  Second-Order  Approximation  (Linear  Interpolation). 819; title: 10.9  Applications of  Multirate Signal Processing  821; title: 10.9.1  Design  of  Phase Shifters. 821; title: 10.9.2  Interfacing of  Digital Systems with  Different Sampling Rates. 823; title: 10.9.3  Implementation  of  Narrowband  Lowpass Filters, 824; title: 10.9.4  Implementation  of  Digital  Filter Banks. 825; title: 10.9.5  Subband Coding of Speech  Signals, 831; title: 10.9.6  Quadrature Mirror Filters. 833; title: 10.9.7  Transmultiplexers. 841; title: 10.9.8  Oversampiing A/D and D/A Conversion. 843; title: 10.10  Summary and References  844; title: Problems  846 Contents; title: 1 I  LINEAR PREDICTION AND OPTIMUM LINEAR FILTERS; title: 11.1  Inno\.rations Representation  of a  Stationary  Random; title: Process  852; title: 11.1.1  Rational Power Spectra. 853; title: 11.1.2  Relationships  Between  the  Filter  Parameters  and  the; title: Autocorrelation Sequence. 855; title: 11.2  Forward and Backward Linear Prediction  857; title: 11.2.1  Forward  Linear Prediction. 857; title: 11.3.2  Backward  Linear  Prediction. 860; title: 11.2.3  The Optimum Reflection  Coefficients for the Lattice  Forward  and; title: Backward  Predictors, 863; title: 11.2.4  Relationship  of  an AR Process  to Linear  Prediction. 864; title: 11.3  Solution  of the  Normal  Equations  864; title: 11.3.1  The Levinson-Durbin  Algorithm. 865; title: 11.3.2  The Schiir Algorithm. S6S; title: 11.4  Properties of  the Linear  Prediction-Error Filters  873; title: 11.5  AR Lattice and ARMA Lattice-Ladder Filters  876; title: 11.5.1  AR Lalticc Structure.  677; title: 11.5.2  ARMA Processes  and Lattice-Ladder  Filters. 878; title: 11.6  Wiener  Filters for Filtering and Prediction  880; title: 11.6.1  FIR  Wiener Filter. 881; title: 11.6.2  Orthogonality  Principle  in  Linear  Mean-Square  Estimat~on. StiJ; title: 11.6.3  IIR Wlener Filter. 885; title: 11.6.4  Noncausal Wiener  Filter. 889; title: 11.7  Summary  and  References  890; title: Problems  892; title: 12  POWER SPECTRUM ESTIMATION  896; title: 2 .   Estimation of  Spectra  from  Finite-Duration  Observations of; title: Signals  896; title: 12.1.1  Computation of  the  Energy Denslty Spectrum. 897; title: 12.1.2  Estimation  of  the  Autocorrelation  and  Power  Spectrum  of; title: Random Signals:  The Periodopram.  902; title: 12.1.3  The Use of  the DFT in  Power Spectrum  Estimation, 906; title: 12.2  Nonparametric Methods for  Power  Spectrum  Estimation  908; title: 12.2.1  The Bartlett Method: Averaging Periodograms.  910; title: 12.2.2  The Welch Method: Averaging Modified  Periodoprams.  911; title: 12.2.3  The  Blackman  and  Tukey Method:  Smoothing  the; title: Periodogram, 913; title: 12.2.4  Performance Characteristics of  Nonparametric Power Spectrum; title: Estimators.  976 Contents; title: 12.2.5  Computational  Requirements  of  Nonparametric  Power Spectrum; title: Estimates, 919; title: 12.3  Parametric  Methods for Power Spectrum Estimation  920; title: 12.3.1  Relationships Between  the  Autocorrelation  and  the Model; title: Parameters, 923; title: 12.3.2  The Yule-Walker  Method for the AR Model Parameters. 925; title: 12.3.3  The Burg Method for the AR Model  Parameters.  975; title: 12.3.4  Unconstrained  Least-Squares  Method  for the  AR  Model; title: Parameters, 929; title: 12.3.5  Sequential Estimation Methods for the AR Model Parameters, 930; title: 12.3.6  Selection  of  AR Model Order, 931; title: 12.3.7  MA Model for Power Spectrum Estimation, 933; title: 12.3.8  ARMA Model for Power Spectrum  Estimation. 931; title: 12.3.9  Some Experimental  Results. 936; title: 12.4  Minimum Variance Spectral Estimation  942; title: Eigenanatysis  Algorithms for Spectrum Estimation  946; title: 12.5.1  Pisarenko Harmonic Decomposition Method, 948; title: 12.5.2  Eigen-decomposition  of  the Autocorrelation Matrix for Sinusoids; title: in  White  Noise. 950; title: 12.5.3  MUSIC Algorithm.  951; title: 12.5.4  ESPRIT Algorithm. 953; title: 12.5.5  Order Selection  Crrteria.  955; title: 12.5.6  Experimental  Results. 956; title: 2 . 6   Summary and References  959; title: Problems  960; title: A  RANDOM SIGNALS, CORRELATION FUNCTIONS,  AND POWER; title: SPECTRA  A1; title: 8  RANDOM NUMBER GENERATORS  8 1; title: C  TABLES OF TRANSITION COEFFICIENTS  FOR THE DESIGN OF; title: LINEAR-PHASE FIR FILTERS  C I; title: D  LIST OF MATLAB FUNCTIONS  D l; title: REFERENCES  AND BlBLlOGRAPHY  R1; title: INDEX  I1