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国外大学数字信号处理教材 3th pdf版
This edition may be sold only in those countries to which it is consigned by Prentice-Hall International. It is not to be reexported and it is not for sale in the U.S.A. Mexico, or Canada c 1996 by Prentice-Hall, Inc Simon schuster/A Viacom Company Upper Saddle River, New Jersey 07458 All rights reserved. No part of this book may be reproduced. in any form or by any means, without permission in writing from the publisher The author and publisher of this book have used their best efforts in preparing this book. These efforts include the development, research and testing of the theories and programs to determine their effectiveness. The author and publisher make no warranty of any kind, expressed or implied. with regard to these programs or the documentation contained in this book. The author and publisher shall not be liable in any event for incidental or consequential damages in connection with or arising out of the furnishing. performance. or use of these programs Printed in the united states of america ISBN D-13-3433吕-日 Prentice-Hall International(UK) Limited. London Prentice-Hall of A ustralia Pty. Limited, Sydney Prentice-Hall Canada. I Prentice-Hall Hispanoamericana. SA. Mexico Prentice-Hall of India Private Limited. New Delhi Prentice-Hall of Japan, Inc, Tokyo Simon Schuster Asia Pte. Ltd, Singapore Editora Prentice-Hall do Brasil. Ltda. rio de janeiro Prentice-Hall, Inc. Upper Saddie River, New Jersey Contents PREFACE 1 INTRODUCTION 1.1 Signals, Systems and Signa! Processing 2 1.1.1 Basic Elements of a Digital Signal Processing System. 4 1. 1.2 Advantages of Digital over Analog Signal Processing, 5 1.2 Classification of Signals 6 1.2.1 Multichannel and Multidimensional Signals. 7 1.2.2 Continuous-Time Versus Discrete- Time Signals. 8 1.2.3 Continuous-Valued Versus Discrete-Valued Signais. 10 1.2.4 Deterministic Versus Random Signals, 11 1.3 The Concept of Frequency in Continuous-Time and Discrete-Time signals 14 1.3.1 Continuous-Time Sinusoidal Signals. 14 1.3.2 Discrete-Time Sinusoidal Signals. 16 1.3.3 Harmonically Related Complex Exponentials, 19 Analog-to-Digital and Digital-to-Analog Conversion 21 1.4.1 Sampling of Analog Signals 1.4.2 The Sampling Theorem, 29 1.4.3 Quantization of ContinuousAmplitude Signals, 33 1.4.4 Quantization of Sinusoidal Signals, 36 pi 1.4.6 Digital-to-Analog Conversion, 38 1.4.7 Analysis of Digital Signals and Systems Versus Discrete-Time Signals and Systems, 39 1.5 Summary and References 39 Problems 40 Contents 2 DISCRETE-TIME SIGNALS AND SYSTEMS 43 2.1 Discrete-Time Signals 43 2. 1.1 Some Elementary Discrete-Time Signals, 45 2.1.2 Classification of Discrete-Time Signals, 47 2,1. 3 Simple Manipulations of Discrete-Time Signals, 52 2.2 Discrete-Time Systems 56 2.2.1 Input-Output Description of Systems, 56 2.2.2 Block Diagram Representation of Discrete-Time Systems, 59 2.2.3 Classification of Discrete- Time Systems. 62 2.2.4 Interconnection of Discrete-fime Systems, 70 2.3 Analysis of Discrete-Time Linear Time-Invariant Systems 72 2,3. 1 Techniques for the Analysis of Linear Systems, 72 2.3.2 Resolution of a Discrete-Time Signal into Impulses, 74 2.3.3 Response of LtI Systems to Arbitrary Inputs: The Convolution S 2.3.4 Properties of Convolution and the interconnection of ltt Syste 2.3.5 Causal Linear Time-Invariant Systems. 86 2.3.6 Stability of linear Time-Invariant Systems 87 2.3.7 Systems with Finite-Duration and infinite-Duration Impulse Response, 90 Discrete-Time Systems Described by Difference Equations 91 2.4.1 Recursive and nonrecursive Discrete Time Systems, 92 2.4.2 Linear Time-Invariant Systems Characterized by Constant-Coefficient Difference Equations, 95 2.4.3 Solution of Linear Constant-Coefficient Difference Equations. 100 2.4.4 The Impulse Response of a Linear Time-Invariant Recursive System. 108 2.5 Implementation of Discrete-Time Systems 111 2.5. 1 Structures for the realization of linear Time-Invariant Systems. 111 2.5.2 Recursive and Nonrecursive Realizations of Fir Systems, 116 2.6 Correlation of Discrete-Time Signals 118 2.6. 1 Crosscorrelation and autocorrelation Sequences. 120 2.6.2 Properties of the Autocorrelation and Crosscorrelation Sequences. 122 2.63 Correlation of Periodic Sequences, 12 2.6.4 Computation of Correlation Sequences. 130 6.5 Input-Output Correlation Sequences, 131 2.7 Summary and references 134 Problems 135 Contents 3 THE Z-TRANSFORM AND ITS APPLICATION TO THE ANALYSIS OF LTI SYSTEMS 151 The --Transform 151 3.1.1 The Direct --Transform 152 3. 1.2 The inverse --Transform. 160 3.2P ies of the --Transform 161 3.3 Rational --Transforms 172 3.3.1 Poles and Zeros, 172 3.3.3 The System Function of a Linear Time-Invariant System. 187]78 3.3.2 Pole Location and Time- Domain Behavior for Causal Signals 3.4 Inversion of the - Transform 184 3.4.1 The Inverse :-Transform by Contour integration. 184 3.4.2 The Inverse - - Transform by Power Series Expansion. 186 3.4.4 Decomposition of Rational:-Transforms. expansion. 188 3.4.3 The Inverse --Transform by Partial-Fraction E 3.5 The One-sided --Transform 197 3.5. 1 Definition and Properties. 197 3.5.2 Solution of Difference Equations. 201 3.6 Analysis of Linear Time-Invariant Systems in the --Domain 203 36.1R of Systems with Rational System Functions 203 3.6.2 Response of Pole-Zero Systems with Nonzero initial Condilions. 204 3.6.3 Transient and Steady - State responses, 206 3.6.4 Causality and Stability. 208 3.6.5 Pole-Zero Cancellations. 210 3.6.6 Multiple-Order Poles and Stability. 211 3.6.7 The Schur-Cohn Stability Test, 213 3.6.8 Stabilitv of Second-Order Svstems. 215 3.7 Summary and References 219 Problems 220 4 FREQUENCY ANALYSIS OF SIGNALS AND SYSTEMS 4.1 Frequency Al g als 230 4.1.1 The Fourier Series for Continuous-Time Periodic Signals. 232 4. 1. 2 Power Density s of periodic sig 4.1.3 The Fourier Transform for Continuous-Time aperiodic Signals, 240 4.1.4 Energy Density Spectrum of Aperiodic Signals. 243 4.2F ncy Analysis of Discrete-Time Signals 247 4.2.1 The Fourier Series for Discrete-Time Periodic Signals, 247 Contents 4.2.2 Power Density Spectrum of Periodic Signals. 250 4.2.3 The Fourier Transform of Discrete-Time Aperiodic Signals. 253 4.2.4 Convergence of the Fourier Transform. 256 4.2.5 Energy Density Spectrum of Aperiodic Signals, 260 4. 2.6 Relationship of the Fourier Transform to the z-Transform. 264 4.2.7 The Cepstrum. 26.5 4.2.8 The Fourier Transform of Signals with Poles on the Unit Circle. 267 4.2.9 The Sampling Theorem Revisited, 269 4.2.10 Frequency-Domain Classification of Signals: The Concept of Bandwidth. 279 4.2.12 Physical and Mathematical Dualities. 202 gnals. 282 4.2.11 The Frequency Ranges of Some Natural Si 3 Properties of the Fourier Transform for Discrete-Time Signals 286 4.3.1 Symmetry Properties of the Fourier Transform, 287 4.3.2 Fourier Transform Theorems and Properties. 294 4. 4 Frequency-Domain Characteristics of Linear Time-Invariant Systems 305 4. 4.1 Response to Complex Exponential and Sinusoidal Signals: The Frequency Response Function. 306 4.4.2 Steady-State and Transient Response to Sinusoidal Input Signals. 314 4.4.3 Steady-State Response to Periodic Input Signals. 315 4.4.4 Response Lo Aperiodic Input Signals. 316 4.4.5 Relationships Between the System Function and the frequency Response F unction 319 4.4.6 Computation of the Frequency Response Function. 321 4.4.7 Input-Output Correlation Functions and Spectra, 325 4.4.8 Correlation Functions and Power Spectra for Random Input Signals. 327 4.5 Linear Time-Invariant Systems as Frequency - Selective Filters 330 4.5.1 Ideal Filter Characteristics, 331 4.5.2 Lowpass, Highpass and Bandpass Filters, 333 4.5.3 Digital Resonators, 340 4.5.4 Notch Filters. 343 4.5.5 Comb Fitters. 345 4.5.6 All-Pass Filters. 350 4.5.7 Digital Sinusoidal Oscillators. 352 4.6 Inverse Systems and Deconvolution 355 4.6.1 Invertibility of Linear Time-Invariant Systems, 356 4.6.2 Minimum-Phase. Maximum-Phase, and Mixed-Phase Systems. 359 4.6.3 System Identification and Deconvolution 363 4.6.4 Homomorphic Deconvolution. 36.5 Contents 4.7 Summary and References 367 Problems 368 5 THE DISCRETE FOURIER TRANSFORM: ITS PROPERTIES AND APPLICATIONS 394 5.1 Frequency Domain Sampling: The Discrete Fourier Transform 394 5.1. 1 Frequency-Domain Sampling and Reconstruction of Discrete- Time signais. 394 5.1.2 The Discrete Fourier Transform(DFT). 399 5.1.3 The DFt as a Linear Transformation. 403 5.1.4 Relationship of the dFt to Other Transforms, 407 5.2 Properties of the DFT 409 5.2. 1 Periodicity, Linearity and Symmetry Properties, 410 5.2.2 Multiplication of two DFTs and Circular Convolution. 415 5.2.3 Additiona! DFT Properties, 421 5.3 Linear Filtering methods based on the dft 425 5.3. 1 Use of the dft in Linear Filtering. 426 5.3.2 Filtering of Long Data Sequences. 430 Frequency Analysis of Signals Using the DFT 433 5 Summary and References 440 6 EFFICIENT COMPUTATION OF THE DFT: FAST FOURIER TRANSFORM ALGORITHMS 448 6.1 Efficient Computation of the DFT: FFT Algorithms 448 6.1.1 Direct Computation of the dFT. 449 6. 1.2 Divide-and-Conquer Approach to Computation of the DFT. 450 6. 1.3 Radix-2 FFT Algorithms. 456 6.1.4 Radix-4 FFT Algorithms. 465 6.1.5 Split-Radix FFT Algorithms, 470 6. 1.6 Implementation of FFT Algorithms. 473 6. 2 Applications of FFT Algorithms 475 6. 2. 1 Efficient Computation of the dFt of Two real Sequences. 475 6.2.2 Efficient Computation of the dFf of a 2N-Point Real Sequence, 476 6.2.3 Use of the FFT Algorithm in Linear Filtering and Correlation 477 6.3 A Linear Filtering Approach to Computation of the DFT 479 6.3.1 The Goertzel Algorithm, 480 6.3.2 The Chirp-z Transform Algorithm, 482 6.4 Quantization Effects in the Computation of the dft 486 6.4.1 Quantization Errors in the Direct Computation of the DFT. 487 6.4.2 Quantization Errors in FFT Algorithms. 489 6.5 Summary and References 493 Problems 494 7 MPLEMENTATON OF DISCRETE-TIME SYSTEMS 500 7. 1 Structures for the Realization of Discrete-Time Systems 500 7.2 Structures for FIR Systems 502 7. 2.2 Cascade-Form Structures. 504 7. 2.3 Frequency-Sampling Structures 7.2.4 Lattice Structure. 511 7.3 Structures for Iir Systems 519 7.3.2 Signal Flow Graphs and Transposed Structures. 521 7.3.4 Paralle]-Form structures 529 Lattice and Lattice- Ladder Structures for IiR Syslems. 531 State-Space Svstem Analysis and Structures 539 7.4.1 State-Space Descriptions of Systems Characterized by Difference Equations. 540 7.4.2 Solution of the State- Space Equations. 543 7.4.3 Relationships Between Input-Output and State-Space Descriptions, 545 7.4.4 State-Space Analysis in the z-Domain, 550 7.4.5 Additional State-Space Structures. 554 5 Representation of Numbers 556 7.5.1 Fixed-Point Representation of Numbers 557 7.5.2 Binary Floating-Point Representation of Numbers. 561 7.5.3 Errors Resulting from Rounding and Truncation. 564 7.6 Quantization of Filter Coefficients 569 7.6.1 Analysis of Sensitivity to Quantization of Filter Coefficients 569 7.6.2 Quantization of Coefficients in FIR Filters, 578 7.7 Round-Off Effects in Digital Filters 582 7.7.1 Limit-Cycle Oscillations in Recursive Systems. 583 7.7. 2 Scaling to Prevent Overflow. 588 7.7. 3 Statistical Characterization of Quantization Effects in Fixed-Point Realizations of Digital Filters 590 7.8 Summary and References 598 Problems 600 Contents 8 DESIGN OF DIGITAL FILTERS 614 8. 1 General Considerations 614 8. 1.1 Causality and its implications, 615 8.1.2 Characteristics of Practical Frequency-Selective Filters. 619 8.2 Design of FIR Filters 620 8.2.1 Symmetric and Antisymmetric FIR Filters, 620 8.2.2 Design of Linear-Phase FIR Filters Using Windows, 62 8.2.3 Design of Linear-Phase FIR Filters by the Frequency-Sampling Method, 630 8.2.4 Design of Optimum Equiripple Linear-Phase FIR Filters. 637 8.2.5 Design of FIR Differentiators, 652 8.2.6 Design of hilbert Transformers. 657 8.2.7 Comparison of Design Methods for Linear-Phase FIR Filters, 662 8.3 Design of IIR Filters From Analog Filters 666 8.3.1 IIR Filter Design by Approximation of Derivatives. 667 8.3.2 IIR Filter Design by Impulse Invariance 671 8.3.3 IIR Filter Design by the Bilinear Transformation. 676 8.3.4 The Matched-- Transformation. 681 8.3.5 Characteristics of Commonly Used Analog Filters. 681 8.3.6 Some Examples of Digital Filter Designs Based on the Bilinear 69 8.4 Frequency Transformations 692 84.1F Transformations in the Analog Domain, 693 8.4.2 Frequency Transformations in the d Domain, 698 8.5 Design of Digital Filters Based on Least-Squares Method 701 8.5.1 Pade approximation method. 701 8.5.2 Least-Squares Design Methods, 706 8.5.3 FIR Least-Squares Inverse(Wiener) Filters, 711 8.5.4 Design of IIR Filters in the Frequency Domain, 719 8.6 Summary and References 724 Problems 726 9 SAMPLING AND RECONSTRUCTION OF SIGNALS 738 9.1 Sampling of Bandpass Signals 738 9.1.1 Representation of Bandpass Signals, 738 9.1.2 Sampling of Bandpass Signals, 742 9.1.3 Discrete-Time Processing of Continuous-Time Signals, 746 9 Analog-to-Digital Conversion 748 9.2.1 Sample-and-Hold. 748 9.2.2 Quantization and Coding, 750 .2.3 Analysis of Quantization Errors 753 9.2.4 Oversampling A/D Converters, 756 【实例截图】
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国外大学数字信号处理教材 3th pdf版
This edition may be sold only in those countries to which it is consigned by Prentice-Hall International. It is not to be reexported and it is not for sale in the U.S.A. Mexico, or Canada c 1996 by Prentice-Hall, Inc Simon schuster/A Viacom Company Upper Saddle River, New Jersey 07458 All rights reserved. No part of this book may be reproduced. in any form or by any means, without permission in writing from the publisher The author and publisher of this book have used their best efforts in preparing this book. These efforts include the development, research and testing of the theories and programs to determine their effectiveness. The author and publisher make no warranty of any kind, expressed or implied. with regard to these programs or the documentation contained in this book. The author and publisher shall not be liable in any event for incidental or consequential damages in connection with or arising out of the furnishing. performance. or use of these programs Printed in the united states of america ISBN D-13-3433吕-日 Prentice-Hall International(UK) Limited. London Prentice-Hall of A ustralia Pty. Limited, Sydney Prentice-Hall Canada. I Prentice-Hall Hispanoamericana. SA. Mexico Prentice-Hall of India Private Limited. New Delhi Prentice-Hall of Japan, Inc, Tokyo Simon Schuster Asia Pte. Ltd, Singapore Editora Prentice-Hall do Brasil. Ltda. rio de janeiro Prentice-Hall, Inc. Upper Saddie River, New Jersey Contents PREFACE 1 INTRODUCTION 1.1 Signals, Systems and Signa! Processing 2 1.1.1 Basic Elements of a Digital Signal Processing System. 4 1. 1.2 Advantages of Digital over Analog Signal Processing, 5 1.2 Classification of Signals 6 1.2.1 Multichannel and Multidimensional Signals. 7 1.2.2 Continuous-Time Versus Discrete- Time Signals. 8 1.2.3 Continuous-Valued Versus Discrete-Valued Signais. 10 1.2.4 Deterministic Versus Random Signals, 11 1.3 The Concept of Frequency in Continuous-Time and Discrete-Time signals 14 1.3.1 Continuous-Time Sinusoidal Signals. 14 1.3.2 Discrete-Time Sinusoidal Signals. 16 1.3.3 Harmonically Related Complex Exponentials, 19 Analog-to-Digital and Digital-to-Analog Conversion 21 1.4.1 Sampling of Analog Signals 1.4.2 The Sampling Theorem, 29 1.4.3 Quantization of ContinuousAmplitude Signals, 33 1.4.4 Quantization of Sinusoidal Signals, 36 pi 1.4.6 Digital-to-Analog Conversion, 38 1.4.7 Analysis of Digital Signals and Systems Versus Discrete-Time Signals and Systems, 39 1.5 Summary and References 39 Problems 40 Contents 2 DISCRETE-TIME SIGNALS AND SYSTEMS 43 2.1 Discrete-Time Signals 43 2. 1.1 Some Elementary Discrete-Time Signals, 45 2.1.2 Classification of Discrete-Time Signals, 47 2,1. 3 Simple Manipulations of Discrete-Time Signals, 52 2.2 Discrete-Time Systems 56 2.2.1 Input-Output Description of Systems, 56 2.2.2 Block Diagram Representation of Discrete-Time Systems, 59 2.2.3 Classification of Discrete- Time Systems. 62 2.2.4 Interconnection of Discrete-fime Systems, 70 2.3 Analysis of Discrete-Time Linear Time-Invariant Systems 72 2,3. 1 Techniques for the Analysis of Linear Systems, 72 2.3.2 Resolution of a Discrete-Time Signal into Impulses, 74 2.3.3 Response of LtI Systems to Arbitrary Inputs: The Convolution S 2.3.4 Properties of Convolution and the interconnection of ltt Syste 2.3.5 Causal Linear Time-Invariant Systems. 86 2.3.6 Stability of linear Time-Invariant Systems 87 2.3.7 Systems with Finite-Duration and infinite-Duration Impulse Response, 90 Discrete-Time Systems Described by Difference Equations 91 2.4.1 Recursive and nonrecursive Discrete Time Systems, 92 2.4.2 Linear Time-Invariant Systems Characterized by Constant-Coefficient Difference Equations, 95 2.4.3 Solution of Linear Constant-Coefficient Difference Equations. 100 2.4.4 The Impulse Response of a Linear Time-Invariant Recursive System. 108 2.5 Implementation of Discrete-Time Systems 111 2.5. 1 Structures for the realization of linear Time-Invariant Systems. 111 2.5.2 Recursive and Nonrecursive Realizations of Fir Systems, 116 2.6 Correlation of Discrete-Time Signals 118 2.6. 1 Crosscorrelation and autocorrelation Sequences. 120 2.6.2 Properties of the Autocorrelation and Crosscorrelation Sequences. 122 2.63 Correlation of Periodic Sequences, 12 2.6.4 Computation of Correlation Sequences. 130 6.5 Input-Output Correlation Sequences, 131 2.7 Summary and references 134 Problems 135 Contents 3 THE Z-TRANSFORM AND ITS APPLICATION TO THE ANALYSIS OF LTI SYSTEMS 151 The --Transform 151 3.1.1 The Direct --Transform 152 3. 1.2 The inverse --Transform. 160 3.2P ies of the --Transform 161 3.3 Rational --Transforms 172 3.3.1 Poles and Zeros, 172 3.3.3 The System Function of a Linear Time-Invariant System. 187]78 3.3.2 Pole Location and Time- Domain Behavior for Causal Signals 3.4 Inversion of the - Transform 184 3.4.1 The Inverse :-Transform by Contour integration. 184 3.4.2 The Inverse - - Transform by Power Series Expansion. 186 3.4.4 Decomposition of Rational:-Transforms. expansion. 188 3.4.3 The Inverse --Transform by Partial-Fraction E 3.5 The One-sided --Transform 197 3.5. 1 Definition and Properties. 197 3.5.2 Solution of Difference Equations. 201 3.6 Analysis of Linear Time-Invariant Systems in the --Domain 203 36.1R of Systems with Rational System Functions 203 3.6.2 Response of Pole-Zero Systems with Nonzero initial Condilions. 204 3.6.3 Transient and Steady - State responses, 206 3.6.4 Causality and Stability. 208 3.6.5 Pole-Zero Cancellations. 210 3.6.6 Multiple-Order Poles and Stability. 211 3.6.7 The Schur-Cohn Stability Test, 213 3.6.8 Stabilitv of Second-Order Svstems. 215 3.7 Summary and References 219 Problems 220 4 FREQUENCY ANALYSIS OF SIGNALS AND SYSTEMS 4.1 Frequency Al g als 230 4.1.1 The Fourier Series for Continuous-Time Periodic Signals. 232 4. 1. 2 Power Density s of periodic sig 4.1.3 The Fourier Transform for Continuous-Time aperiodic Signals, 240 4.1.4 Energy Density Spectrum of Aperiodic Signals. 243 4.2F ncy Analysis of Discrete-Time Signals 247 4.2.1 The Fourier Series for Discrete-Time Periodic Signals, 247 Contents 4.2.2 Power Density Spectrum of Periodic Signals. 250 4.2.3 The Fourier Transform of Discrete-Time Aperiodic Signals. 253 4.2.4 Convergence of the Fourier Transform. 256 4.2.5 Energy Density Spectrum of Aperiodic Signals, 260 4. 2.6 Relationship of the Fourier Transform to the z-Transform. 264 4.2.7 The Cepstrum. 26.5 4.2.8 The Fourier Transform of Signals with Poles on the Unit Circle. 267 4.2.9 The Sampling Theorem Revisited, 269 4.2.10 Frequency-Domain Classification of Signals: The Concept of Bandwidth. 279 4.2.12 Physical and Mathematical Dualities. 202 gnals. 282 4.2.11 The Frequency Ranges of Some Natural Si 3 Properties of the Fourier Transform for Discrete-Time Signals 286 4.3.1 Symmetry Properties of the Fourier Transform, 287 4.3.2 Fourier Transform Theorems and Properties. 294 4. 4 Frequency-Domain Characteristics of Linear Time-Invariant Systems 305 4. 4.1 Response to Complex Exponential and Sinusoidal Signals: The Frequency Response Function. 306 4.4.2 Steady-State and Transient Response to Sinusoidal Input Signals. 314 4.4.3 Steady-State Response to Periodic Input Signals. 315 4.4.4 Response Lo Aperiodic Input Signals. 316 4.4.5 Relationships Between the System Function and the frequency Response F unction 319 4.4.6 Computation of the Frequency Response Function. 321 4.4.7 Input-Output Correlation Functions and Spectra, 325 4.4.8 Correlation Functions and Power Spectra for Random Input Signals. 327 4.5 Linear Time-Invariant Systems as Frequency - Selective Filters 330 4.5.1 Ideal Filter Characteristics, 331 4.5.2 Lowpass, Highpass and Bandpass Filters, 333 4.5.3 Digital Resonators, 340 4.5.4 Notch Filters. 343 4.5.5 Comb Fitters. 345 4.5.6 All-Pass Filters. 350 4.5.7 Digital Sinusoidal Oscillators. 352 4.6 Inverse Systems and Deconvolution 355 4.6.1 Invertibility of Linear Time-Invariant Systems, 356 4.6.2 Minimum-Phase. Maximum-Phase, and Mixed-Phase Systems. 359 4.6.3 System Identification and Deconvolution 363 4.6.4 Homomorphic Deconvolution. 36.5 Contents 4.7 Summary and References 367 Problems 368 5 THE DISCRETE FOURIER TRANSFORM: ITS PROPERTIES AND APPLICATIONS 394 5.1 Frequency Domain Sampling: The Discrete Fourier Transform 394 5.1. 1 Frequency-Domain Sampling and Reconstruction of Discrete- Time signais. 394 5.1.2 The Discrete Fourier Transform(DFT). 399 5.1.3 The DFt as a Linear Transformation. 403 5.1.4 Relationship of the dFt to Other Transforms, 407 5.2 Properties of the DFT 409 5.2. 1 Periodicity, Linearity and Symmetry Properties, 410 5.2.2 Multiplication of two DFTs and Circular Convolution. 415 5.2.3 Additiona! DFT Properties, 421 5.3 Linear Filtering methods based on the dft 425 5.3. 1 Use of the dft in Linear Filtering. 426 5.3.2 Filtering of Long Data Sequences. 430 Frequency Analysis of Signals Using the DFT 433 5 Summary and References 440 6 EFFICIENT COMPUTATION OF THE DFT: FAST FOURIER TRANSFORM ALGORITHMS 448 6.1 Efficient Computation of the DFT: FFT Algorithms 448 6.1.1 Direct Computation of the dFT. 449 6. 1.2 Divide-and-Conquer Approach to Computation of the DFT. 450 6. 1.3 Radix-2 FFT Algorithms. 456 6.1.4 Radix-4 FFT Algorithms. 465 6.1.5 Split-Radix FFT Algorithms, 470 6. 1.6 Implementation of FFT Algorithms. 473 6. 2 Applications of FFT Algorithms 475 6. 2. 1 Efficient Computation of the dFt of Two real Sequences. 475 6.2.2 Efficient Computation of the dFf of a 2N-Point Real Sequence, 476 6.2.3 Use of the FFT Algorithm in Linear Filtering and Correlation 477 6.3 A Linear Filtering Approach to Computation of the DFT 479 6.3.1 The Goertzel Algorithm, 480 6.3.2 The Chirp-z Transform Algorithm, 482 6.4 Quantization Effects in the Computation of the dft 486 6.4.1 Quantization Errors in the Direct Computation of the DFT. 487 6.4.2 Quantization Errors in FFT Algorithms. 489 6.5 Summary and References 493 Problems 494 7 MPLEMENTATON OF DISCRETE-TIME SYSTEMS 500 7. 1 Structures for the Realization of Discrete-Time Systems 500 7.2 Structures for FIR Systems 502 7. 2.2 Cascade-Form Structures. 504 7. 2.3 Frequency-Sampling Structures 7.2.4 Lattice Structure. 511 7.3 Structures for Iir Systems 519 7.3.2 Signal Flow Graphs and Transposed Structures. 521 7.3.4 Paralle]-Form structures 529 Lattice and Lattice- Ladder Structures for IiR Syslems. 531 State-Space Svstem Analysis and Structures 539 7.4.1 State-Space Descriptions of Systems Characterized by Difference Equations. 540 7.4.2 Solution of the State- Space Equations. 543 7.4.3 Relationships Between Input-Output and State-Space Descriptions, 545 7.4.4 State-Space Analysis in the z-Domain, 550 7.4.5 Additional State-Space Structures. 554 5 Representation of Numbers 556 7.5.1 Fixed-Point Representation of Numbers 557 7.5.2 Binary Floating-Point Representation of Numbers. 561 7.5.3 Errors Resulting from Rounding and Truncation. 564 7.6 Quantization of Filter Coefficients 569 7.6.1 Analysis of Sensitivity to Quantization of Filter Coefficients 569 7.6.2 Quantization of Coefficients in FIR Filters, 578 7.7 Round-Off Effects in Digital Filters 582 7.7.1 Limit-Cycle Oscillations in Recursive Systems. 583 7.7. 2 Scaling to Prevent Overflow. 588 7.7. 3 Statistical Characterization of Quantization Effects in Fixed-Point Realizations of Digital Filters 590 7.8 Summary and References 598 Problems 600 Contents 8 DESIGN OF DIGITAL FILTERS 614 8. 1 General Considerations 614 8. 1.1 Causality and its implications, 615 8.1.2 Characteristics of Practical Frequency-Selective Filters. 619 8.2 Design of FIR Filters 620 8.2.1 Symmetric and Antisymmetric FIR Filters, 620 8.2.2 Design of Linear-Phase FIR Filters Using Windows, 62 8.2.3 Design of Linear-Phase FIR Filters by the Frequency-Sampling Method, 630 8.2.4 Design of Optimum Equiripple Linear-Phase FIR Filters. 637 8.2.5 Design of FIR Differentiators, 652 8.2.6 Design of hilbert Transformers. 657 8.2.7 Comparison of Design Methods for Linear-Phase FIR Filters, 662 8.3 Design of IIR Filters From Analog Filters 666 8.3.1 IIR Filter Design by Approximation of Derivatives. 667 8.3.2 IIR Filter Design by Impulse Invariance 671 8.3.3 IIR Filter Design by the Bilinear Transformation. 676 8.3.4 The Matched-- Transformation. 681 8.3.5 Characteristics of Commonly Used Analog Filters. 681 8.3.6 Some Examples of Digital Filter Designs Based on the Bilinear 69 8.4 Frequency Transformations 692 84.1F Transformations in the Analog Domain, 693 8.4.2 Frequency Transformations in the d Domain, 698 8.5 Design of Digital Filters Based on Least-Squares Method 701 8.5.1 Pade approximation method. 701 8.5.2 Least-Squares Design Methods, 706 8.5.3 FIR Least-Squares Inverse(Wiener) Filters, 711 8.5.4 Design of IIR Filters in the Frequency Domain, 719 8.6 Summary and References 724 Problems 726 9 SAMPLING AND RECONSTRUCTION OF SIGNALS 738 9.1 Sampling of Bandpass Signals 738 9.1.1 Representation of Bandpass Signals, 738 9.1.2 Sampling of Bandpass Signals, 742 9.1.3 Discrete-Time Processing of Continuous-Time Signals, 746 9 Analog-to-Digital Conversion 748 9.2.1 Sample-and-Hold. 748 9.2.2 Quantization and Coding, 750 .2.3 Analysis of Quantization Errors 753 9.2.4 Oversampling A/D Converters, 756 【实例截图】
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