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Essentials of Digital Signal Processing

Book Description

This textbook offers a fresh approach to digital signal processing (DSP) that combines heuristic reasoning and physical appreciation with sound mathematical methods to illuminate DSP concepts and practices. It uses metaphors, analogies and creative explanations, along with examples and exercises to provide deep and intuitive insights into DSP concepts. Practical DSP requires hybrid systems including both discrete- and continuous-time components. This book follows a holistic approach and presents discrete-time processing as a seamless continuation of continuous-time signals and systems, beginning with a review of continuous-time signals and systems, frequency response, and filtering. The synergistic combination of continuous-time and discrete-time perspectives leads to a deeper appreciation and understanding of DSP concepts and practices. • For upper-level undergraduates • Illustrates concepts with 500 high-quality figures, more than 170 fully worked examples, and hundreds of end-of-chapter problems, more than 150 drill exercises, including complete and detailed solutions • Seamlessly integrates MATLAB throughout the text to enhance learning

Table of Contents

  1. Cover
  2. Half-title page
  3. Title
  4. Copyright
  5. Contents
  6. Preface
  7. 1 Review of Continuous-Time Signals and Systems
    1. 1.1 Signals and Signal Categorizations
      1. 1.1.1 Continuous-Time and Discrete-Time Signals
      2. 1.1.2 Analog and Digital Signals
    2. 1.2 Operations on the Independent CT Variable
      1. 1.2.1 CT Time Shifting
      2. 1.2.2 CT Time Scaling
      3. 1.2.3 CT Time Reversal
      4. 1.2.4 Combined CT Time Shifting and Scaling
    3. 1.3 CT Signal Models
      1. 1.3.1 CT Unit Step Function u(t)
      2. 1.3.2 CT Unit Gate Function Π(t)
      3. 1.3.3 CT Unit Triangle Function Λ(t)
      4. 1.3.4 CT Unit Impulse Function δ(t)
      5. 1.3.5 CT Exponential Function est
      6. 1.3.6 CT Interpolation Function sinc(t)
    4. 1.4 CT Signal Classifications
      1. 1.4.1 Causal, Noncausal, and Anti-Causal CT Signals
      2. 1.4.2 Real and Imaginary CT Signals
      3. 1.4.3 Even and Odd CT Signals
      4. 1.4.4 Periodic and Aperiodic CT Signals
      5. 1.4.5 CT Energy and Power Signals
      6. 1.4.6 Deterministic and Probabilistic Signals
    5. 1.5 CT Systems and Properties
      1. 1.5.1 Linearity
      2. 1.5.2 Time Invariance
      3. 1.5.3 The Zero-State Response of an LTIC System
      4. 1.5.4 Causality
      5. 1.5.5 Stability
    6. 1.6 Foundations of Frequency-Domain Analysis
      1. 1.6.1 LTIC System Response to an Everlasting Exponential est
    7. 1.7 The Fourier Series
      1. 1.7.1 Exponential Form of the Fourier Series
      2. 1.7.2 Trigonometric and Compact Trigonometric Forms
      3. 1.7.3 Convergence of a Series
    8. 1.8 The Fourier Transform
    9. 1.9 Fourier Transform Properties
      1. 1.9.1 Duality Property
      2. 1.9.2 Linearity Property
      3. 1.9.3 Complex-Conjugation Property
      4. 1.9.4 Scaling Property
      5. 1.9.5 Time-Shifting Property
      6. 1.9.6 Time-Differentiation and Time-Integration Properties
      7. 1.9.7 Time-Domain Convolution Property
      8. 1.9.8 Correlation and the Correlation Property
      9. 1.9.9 Extending Fourier Transform Properties to the Fourier Series
    10. 1.10 The Laplace Transform
      1. 1.10.1 Connection between the Fourier and Laplace Transforms
      2. 1.10.2 Laplace Transform Properties
    11. 1.11 Summary
  8. 2 Continuous-Time Analog Filters
    1. 2.1 Frequency Response of an LTIC System
      1. 2.1.1 Pole-Zero Plots
    2. 2.2 Signal Transmission through LTIC Systems
      1. 2.2.1 Distortionless Transmission
      2. 2.2.2 Real Bandpass Systems and Group Delay
    3. 2.3 Ideal and Realizable Filters
    4. 2.4 Data Truncation by Windows
      1. 2.4.1 Impairments Caused by Windowing
      2. 2.4.2 Lowpass Filter Design Using Windows
      3. 2.4.3 Remedies for Truncation Impairments
      4. 2.4.4 Common Window Functions
    5. 2.5 Specification of Practical Filters
    6. 2.6 Analog Filter Transformations
      1. 2.6.1 Lowpass-to-Lowpass Transformation
      2. 2.6.2 Lowpass-to-Highpass Transformation
      3. 2.6.3 Lowpass-to-Bandpass Transformation
      4. 2.6.4 Lowpass-to-Bandstop Transformation
    7. 2.7 Practical Filter Families
      1. 2.7.1 Butterworth Filters
      2. 2.7.2 Chebyshev Filters
      3. 2.7.3 Inverse Chebyshev Filters
      4. 2.7.4 Elliptic Filters
      5. 2.7.5 Bessel-Thomson Filters
    8. 2.8 Summary
  9. 3 Sampling: The Bridge from Continuous to Discrete
    1. 3.1 Sampling and the Sampling Theorem
      1. 3.1.1 Practical Sampling
    2. 3.2 Signal Reconstruction
    3. 3.3 Practical Difficulties in Sampling and Reconstruction
      1. 3.3.1 Aliasing in Sinusoids
    4. 3.4 Sampling of Bandpass Signals
    5. 3.5 Time-Sampling Dual: The Spectral Sampling Theorem
    6. 3.6 Analog-to-Digital Conversion
      1. 3.6.1 Analog-to-Digital Converter Transfer Characteristics
      2. 3.6.2 Analog-to-Digital Converter Errors
      3. 3.6.3 Analog-to-Digital Converter Implementations
    7. 3.7 Digital-to-Analog Conversion
      1. 3.7.1 Sources of Distortion in Signal Reconstruction
    8. 3.8 Summary
  10. 4 Discrete-Time Signals and Systems
    1. 4.1 Operations on the Independent DT Variable
      1. 4.1.1 DT Time Shifting
      2. 4.1.2 DT Time Reversal
      3. 4.1.3 DT Time Scaling: Sampling Rate Conversion
    2. 4.2 DT Signal Models
      1. 4.2.1 DT Unit Step Function u[n]
      2. 4.2.2 DT Unit Impulse Function δ[n]
      3. 4.2.3 DT Exponential Function zn
    3. 4.3 DT Signal Classifications
      1. 4.3.1 Causal, Noncausal, and Anti-Causal DT Signals
      2. 4.3.2 Real and Imaginary DT Signals
      3. 4.3.3 Even and Odd DT Signals
      4. 4.3.4 Periodic and Aperiodic DT Signals
      5. 4.3.5 DT Energy and Power Signals
    4. 4.4 DT Systems and Examples
      1. 4.4.1 The Order and General Form of Difference Equations
      2. 4.4.2 Kinship of Difference Equations to Differential Equations
      3. 4.4.3 Advantages of Digital Signal Processing
    5. 4.5 DT System Properties
      1. 4.5.1 Time Invariance
      2. 4.5.2 Linearity
      3. 4.5.3 The Zero-State Response of an LTID System
      4. 4.5.4 Causality
      5. 4.5.5 Stability
      6. 4.5.6 Memory
      7. 4.5.7 Invertibility
    6. 4.6 Digital Resampling
    7. 4.7 Summary
  11. 5 Time-Domain Analysis of Discrete-Time Systems
    1. 5.1 Iterative Solutions to Difference Equations
    2. 5.2 Operator Notation
    3. 5.3 The Zero-Input Response
      1. 5.3.1 Insights into the Zero-Input Behavior of a System
    4. 5.4 The Unit Impulse Response
      1. 5.4.1 Closed-Form Solution of the Impulse Response
    5. 5.5 The Zero-State Response
      1. 5.5.1 Convolution Sum Properties
      2. 5.5.2 Graphical Procedure for the Convolution Sum
      3. 5.5.3 Interconnected Systems
      4. 5.5.4 LTID System Response to an Everlasting Exponential zn
    6. 5.6 Total Response
    7. 5.7 System Stability
      1. 5.7.1 External (BIBO) Stability
      2. 5.7.2 Internal (Asymptotic) Stability
    8. 5.8 Intuitive Insights into System Behavior
      1. 5.8.1 Dependence of System Behavior on Characteristic Modes
      2. 5.8.2 Response Time of a System: The System Time Constant
      3. 5.8.3 Time Constant and Rise Time of a System
      4. 5.8.4 Time Constant and Filtering
      5. 5.8.5 Time Constant and Pulse Dispersion
      6. 5.8.6 The Resonance Phenomenon
    9. 5.9 Classical Solution of Linear Difference Equations
    10. 5.10 Summary
  12. 6 Discrete-Time Fourier Analysis
    1. 6.1 The Discrete-Time Fourier Transform
      1. 6.1.1 The Nature of Fourier Spectra
      2. 6.1.2 Obtaining the DTFT from the CTFT
      3. 6.1.3 DTFT Tables and the Nuisance of Periodicity
    2. 6.2 Properties of the DTFT
      1. 6.2.1 Duality
      2. 6.2.2 Linearity Property
      3. 6.2.3 Complex-Conjugation Property
      4. 6.2.4 Time Scaling and the Time-Reversal Property
      5. 6.2.5 Time-Shifting Property
      6. 6.2.6 Frequency-Differentiation Property
      7. 6.2.7 Time-Domain and Frequency-Domain Convolution Properties
      8. 6.2.8 Correlation and the Correlation Property
    3. 6.3 LTIDSystem Analysis by the DTFT
      1. 6.3.1 Distortionless Transmission
      2. 6.3.2 Ideal and Realizable Filters
    4. 6.4 Connection between the DTFT and the CTFT
    5. 6.5 Digital Processing of Analog Signals
      1. 6.5.1 A Mathematical Representation
      2. 6.5.2 Time-Domain Criterion: The Impulse Invariance Method
    6. 6.6 Digital Resampling: A Frequency-Domain Perspective
      1. 6.6.1 Using Bandlimited Interpolation to Understand Resampling
      2. 6.6.2 Downsampling and Decimation
      3. 6.6.3 Interpolation and Upsampling
      4. 6.6.4 Time-Domain Characterizations
      5. 6.6.5 Fractional Sampling Rate Conversion
    7. 6.7 Generalization of the DTFT to the z-Transform
    8. 6.8 Summary
  13. 7 Discrete-Time System Analysis Using the z-Transform
    1. 7.1 The z-Transform
      1. 7.1.1 The Bilateral z-Transform
      2. 7.1.2 The Unilateral z-Transform
    2. 7.2 The Inverse z-Transform
      1. 7.2.1 Inverse z-Transform by Power Series Expansion
    3. 7.3 Properties of the z-Transform
      1. 7.3.1 Linearity Property
      2. 7.3.2 Complex-Conjugation Property
      3. 7.3.3 Time Scaling and the Time-Reversal Property
      4. 7.3.4 Time-Shifting Property
      5. 7.3.5 z-Domain Scaling Property
      6. 7.3.6 z-Domain Differentiation Property
      7. 7.3.7 Time-Domain Convolution Property
      8. 7.3.8 Initial and Final Value Theorems
    4. 7.4 z-Transform Solution of Linear Difference Equations
      1. 7.4.1 Zero-State Response of LTID Systems: The Transfer Function
    5. 7.5 Block Diagrams and System Realization
      1. 7.5.1 Direct Form Realizations
      2. 7.5.2 Transposed Realizations
      3. 7.5.3 Cascade and Parallel Realizations
    6. 7.6 Frequency Response of Discrete-Time Systems
      1. 7.6.1 Frequency Response from Pole-Zero Locations
    7. 7.7 Finite Word-Length Effects
      1. 7.7.1 Finite Word-Length Effects on Poles and Zeros
      2. 7.7.2 Finite Word-Length Effects on Frequency Response
    8. 7.8 Connection between the Laplace and z-Transforms
    9. 7.9 Summary
  14. 8 Digital Filters
    1. 8.1 Infinite Impulse Response Filters
      1. 8.1.1 The Impulse Invariance Method Revisited
      2. 8.1.2 The Bilinear Transform
      3. 8.1.3 The Bilinear Transform with Prewarping
      4. 8.1.4 Highpass, Bandpass, and Bandstop Filters
      5. 8.1.5 Realization of IIR Filters
    2. 8.2 Finite Impulse Response Filters
      1. 8.2.1 Linear Phase FIR Filters
      2. 8.2.2 Realization of FIR Filters
      3. 8.2.3 Windowing in FIR Filters
      4. 8.2.4 Time-Domain Methods of FIR Filter Design
      5. 8.2.5 Window Method FIR Filter Design for Given Specifications
      6. 8.2.6 Frequency-Domain Methods of FIR Filter Design
      7. 8.2.7 Frequency-Weighted Least-Squares FIR Filter Design
    3. 8.3 Summary
  15. 9 Discrete Fourier Transform
    1. 9.1 The Discrete Fourier Transform
      1. 9.1.1 The Picket Fence Effect and Zero Padding
      2. 9.1.2 Matrix Representation of the DFT and Its Inverse
      3. 9.1.3 DFT Interpolation to Obtain the DTFT
    2. 9.2 Uniqueness: Why Confine x[n] to 0 ≤ n ≤ N – 1?
      1. 9.2.1 Modulo-N Operation
      2. 9.2.2 Circular Representation of an N-Length Sequence
    3. 9.3 Properties of the DFT
      1. 9.3.1 Duality Property
      2. 9.3.2 Linearity Property
      3. 9.3.3 Complex-Conjugation Property
      4. 9.3.4 Time-Reversal Property
      5. 9.3.5 Circular Shifting Properties
      6. 9.3.6 Circular Convolution Properties
      7. 9.3.7 Circular Correlation Property
    4. 9.4 Graphical Interpretation of Circular Convolution
      1. 9.4.1 Circular and Linear Convolution
      2. 9.4.2 Aliasing in Circular Convolution
    5. 9.5 Discrete-Time Filtering Using the DFT
      1. 9.5.1 Block Convolution
    6. 9.6 Goertzel’s Algorithm
    7. 9.7 The Fast Fourier Transform
      1. 9.7.1 Decimation-in-Time Algorithm
      2. 9.7.2 Decimation-in-Frequency Algorithm
    8. 9.8 The Discrete-Time Fourier Series
    9. 9.9 Summary
  16. A MATLAB
  17. B Useful Tables
  18. C Drill Solutions
  19. Index