Digital Signal Processing: Principles, Algorithms and Applications, 5th edition

1. Introduction
   • 1.1 Signals, Systems, and Signal Processing
     • 1.1.1 Basic Elements of a Digital Signal Processing System
     • 1.1.2 Advantages of Digital over Analog Signal Processing
   • 1.2 Classification of Signals
     • 1.2.1 Multichannel and Multidimensional Signals
     • 1.2.2 Continuous-Time Versus Discrete-Time Signals
     • 1.2.3 Continuous-Valued Versus Discrete-Valued Signals
     • 1.2.4 Deterministic Versus Random Signals
   • 1.3 Summary
   • Problems
2. Discrete-Time Signals and Systems
   • 2.1 Discrete-Time Signals
     • 2.1.1 Some Elementary Discrete-Time Signals
     • 2.1.2 Classification of Discrete-Time Signals
     • 2.1.3 Simple Manipulations of Discrete-Time Signals
   • 2.2 Discrete-Time Systems
     • 2.2.1 Input-Output Description of Systems
     • 2.2.2 Block Diagram Representation of Discrete-Time Systems
     • 2.2.3 Classification of Discrete-Time Systems
     • 2.2.4 Interconnection of Discrete-Time Systems
   • 2.3 Analysis of Discrete-Time Linear Time-Invariant Systems
     • 2.3.1 Techniques for the Analysis of Linear Systems
     • 2.3.2 Resolution of a Discrete-Time Signal into Impulses
     • 2.3.3 Response of LTI Systems to Arbitrary Inputs: The Convolution Sum
     • 2.3.4 Properties of Convolution and the Interconnection of LTI Systems
     • 2.3.5 Causal Linear Time-Invariant Systems
     • 2.3.6 Stability of Linear Time-Invariant Systems
     • 2.3.7 Systems with Finite-Duration and Infinite-Duration Impulse Response
   • 2.4 Discrete-Time Systems Described by Difference Equations
     • 2.4.1 Recursive and Nonrecursive Discrete-Time Systems
     • 2.4.2 Linear Time-Invariant Systems Characterized by Constant-Coefficient Difference Equations
     • 2.4.3 Application of LTI Systems for Signal Smoothing
   • 2.5 Implementation of Discrete-Time Systems
     • 2.5.1 Structures for the Realization of Linear Time-Invariant Systems
     • 2.5.2 Recursive and Nonrecursive Realizations of FIR Systems
   • 2.6 Correlation of Discrete-Time Signals
     • 2.6.1 Crosscorrelation and Autocorrelation Sequences
     • 2.6.2 Properties of the Autocorrelation and Crosscorrelation Sequences
     • 2.6.3 Correlation of Periodic Sequences
     • 2.6.4 Input-Output Correlation Sequences
   • 2.7 Summary
   • Problems
   • Computer Problems
3. The z-Transform and Its Application to the Analysis of LTI Systems
   • 3.1 The z-Transform
     • 3.1.1 The Direct z-Transform
     • 3.1.2 The Inverse z-Transform
   • 3.2 Properties of the z-Transform
   • 3.3 Rational z-Transforms
     • 3.3.1 Poles and Zeros
     • 3.3.2 Pole Location and Time-Domain Behavior for Causal Signals
     • 3.3.3 The System Function of a Linear Time-Invariant System
   • 3.4 Inversion of the z-Transform
     • 3.4.1 The Inverse z-Transform by Contour Integration
     • 3.4.2 The Inverse z-Transform by Power Series Expansion
     • 3.4.3 The Inverse z-Transform by Partial-Fraction Expansion
     • 3.4.4 Decomposition of Rational z-Transforms
   • 3.5 Analysis of Linear Time-Invariant Systems in the z-Domain
     • 3.5.1 Response of Systems with Rational System Functions
     • 3.5.2 Transient and Steady-State Responses
     • 3.5.3 Causality and Stability
     • 3.5.4 Pole—Zero Cancellations
     • 3.5.5 Multiple-Order Poles and Stability
     • 3.5.6 Stability of Second-Order Systems
   • 3.6 The One-sided z-Transform
     • 3.6.1 Definition and Properties
     • 3.6.2 Solution of Difference Equations
     • 3.6.3 Response of Pole—Zero Systems with Nonzero Initial Conditions
   • 3.7 Summary
   • Problems
   • Computer Problems
4. Frequency Analysis of Signals
   • 4.1 The Concept of Frequency in Continuous-Time and Discrete-Time Signals
     • 4.1.1 Continuous-Time Sinusoidal Signals
     • 4.1.2 Discrete-Time Sinusoidal Signals
     • 4.1.3 Harmonically Related Complex Exponentials
     • 4.1.4 Sampling of Analog Signals
     • 4.1.5 The Sampling Theorem
   • 4.2 Frequency Analysis of Continuous-Time Signals
     • 4.2.1 The Fourier Series for Continuous-Time Periodic Signals
     • 4.2.2 Power Density Spectrum of Periodic Signals
     • 4.2.3 The Fourier Transform for Continuous-Time Aperiodic Signals
     • 4.2.4 Energy Density Spectrum of Aperiodic Signals
   • 4.3 Frequency Analysis of Discrete-Time Signals
     • 4.3.1 The Fourier Series for Discrete-Time Periodic Signals
     • 4.3.2 Power Density Spectrum of Periodic Signals
     • 4.3.3 The Fourier Transform of Discrete-Time Aperiodic Signals
     • 4.3.4 Convergence of the Fourier Transform
     • 4.3.5 Energy Density Spectrum of Aperiodic Signals
     • 4.3.6 Relationship of the Fourier Transform to the z-Transform
     • 4.3.7 The Cepstrum
     • 4.3.8 The Fourier Transform of Signals with Poles on the Unit Circle
     • 4.3.9 Frequency-Domain Classification of Signals: The Concept of Bandwidth
     • 4.3.10 The Frequency Ranges of Some Natural Signals
   • 4.4 Frequency-Domain and Time-Domain Signal Properties
   • 4.5 Properties of the Fourier Transform for Discrete-Time Signals
     • 4.5.1 Symmetry Properties of the Fourier Transform
     • 4.5.2 Fourier Transform Theorems and Properties
   • 4.6 Summary
   • Problems
   • Computer Problems
5. Frequency-Domain Analysis of LTI Systems
   • 5.1 Frequency-Domain Characteristics of Linear Time-Invariant Systems
     • 5.1.1 Response to Complex Exponential and Sinusoidal Signals: The Frequency Response Function
     • 5.1.2 Steady-State and Transient Response to Sinusoidal Input Signals
     • 5.1.3 Steady-State Response to Periodic Input Signals
     • 5.1.4 Steady-State Response to Aperiodic Input Signals
   • 5.2 Frequency Response of LTI Systems
     • 5.2.1 Frequency Response of a System with a Rational System Function
     • 5.2.2 Computation of the Frequency Response Function
   • 5.3 Correlation Functions and Spectra at the Output of LTI Systems
   • 5.4 Linear Time-Invariant Systems as Frequency-Selective Filters
     • 5.4.1 Ideal Filter Characteristics
     • 5.4.2 Lowpass, Highpass, and Bandpass Filters
     • 5.4.3 Digital Resonators
     • 5.4.4 Notch Filters
     • 5.4.5 Comb Filters
     • 5.4.6 Reverberation Filters
     • 5.4.7 All-Pass Filters
     • 5.4.8 Digital Sinusoidal Oscillators
   • 5.5 Inverse Systems and Deconvolution
     • 5.5.1 Invertibility of Linear Time-Invariant Systems
     • 5.5.2 Minimum-Phase, Maximum-Phase, and Mixed-Phase Systems
     • 5.5.3 System Identification and Deconvolution
     • 5.5.4 Homomorphic Deconvolution
   • 5.6 Summary
   • Problems
   • Computer Problems
6. Sampling and Reconstruction of Signals
   • 6.1 Ideal Sampling and Reconstruction of Continuous-Time Signals
   • 6.2 Discrete-Time Processing of Continuous-Time Signals
   • 6.3 Sampling and Reconstruction of Continuous-Time Bandpass Signals
     • 6.3.1 Uniform or First-Order Sampling
     • 6.3.2 Interleaved or Nonuniform Second-Order Sampling
     • 6.3.3 Bandpass Signal Representations
     • 6.3.4 Sampling Using Bandpass Signal Representations
   • 6.4 Sampling of Discrete-Time Signals
     • 6.4.1 Sampling and Interpolation of Discrete-Time Signals
     • 6.4.2 Representation and Sampling of Bandpass Discrete-Time Signals
   • 6.5 Analog-to-Digital and Digital-to-Analog Converters
     • 6.5.1 Analog-to-Digital Converters
     • 6.5.2 Quantization and Coding
     • 6.5.3 Analysis of Quantization Errors
     • 6.5.4 Digital-to-Analog Converters
   • 6.6 Oversampling A/D and D/A Converters
     • 6.6.1 Oversampling A/D Converters
     • 6.6.2 Oversampling D/A Converters
   • 6.7 Summary
   • Problems
   • Computer Problems
7. The Discrete Fourier Transform: Its Properties and Applications
   • 7.1 Frequency-Domain Sampling: The Discrete Fourier Transform
     • 7.1.1 Frequency-Domain Sampling and Reconstruction of Discrete-Time Signals
     • 7.1.2 The Discrete Fourier Transform (DFT)
     • 7.1.3 The DFT as a Linear Transformation
     • 7.1.4 Relationship of the DFT to Other Transforms
   • 7.2 Properties of the DFT
     • 7.2.1 Periodicity, Linearity, and Symmetry Properties
     • 7.2.2 Multiplication of Two DFTs and Circular Convolution
     • 7.2.3 Additional DFT Properties
   • 7.3 Linear Filtering Methods Based on the DFT
     • 7.3.1 Use of the DFT in Linear Filtering
     • 7.3.2 Filtering of Long Data Sequences
   • 7.4 Frequency Analysis of Signals Using the DFT
   • 7.5 The Short-Time Fourier Transform
   • 7.6 The Discrete Cosine Transform
     • 7.6.1 Forward DCT
     • 7.6.2 Inverse DCT
     • 7.6.3 DCT as an Orthogonal Transform
   • 7.7 Summary
   • Problems
   • Computer Problems
8. Efficient Computation of the DFT: Fast Fourier Transform Algorithms
   • 8.1 Efficient Computation of the DFT: FFT Algorithms
     • 8.1.1 Direct Computation of the DFT
     • 8.1.2 Divide-and-Conquer Approach to Computation of the DFT
     • 8.1.3 Radix-2 FFT Algorithms
     • 8.1.4 Radix-4 FFT Algorithms
     • 8.1.5 Split-Radix FFT Algorithms
     • 8.1.6 Implementation of FFT Algorithms
     • 8.1.7 Sparse FFT Algorithm
   • 8.2 Applications of FFT Algorithms
     • 8.2.1 Efficient Computation of the DFT of Two Real Sequences
     • 8.2.2 Efficient Computation of the DFT of a 2N-Point Real Sequence
     • 8.2.3 Use of the FFT Algorithm in Linear Filtering and Correlation
   • 8.3 A Linear Filtering Approach to Computation of the DFT
     • 8.3.1 The Goertzel Algorithm
     • 8.3.2 The Chirp-z Transform Algorithm
   • 8.4 Quantization Effects in the Computation of the DFT
     • 8.4.1 Quantization Errors in the Direct Computation of the DFT
     • 8.4.2 Quantization Errors in FFT Algorithms
   • 8.5 Summary
   • Problems
   • Computer Problems
9. Implementation of Discrete-Time Systems
   • 9.1 Structures for the Realization of Discrete-Time Systems
   • 9.2 Structures for FIR Systems
     • 9.2.1 Direct-Form Structure
     • 9.2.2 Cascade-Form Structures
     • 9.2.3 Frequency-Sampling Structures
     • 9.2.4 Lattice Structure
   • 9.3 Structures for IIR Systems
     • 9.3.1 Direct-Form Structures
     • 9.3.2 Signal Flow Graphs and Transposed Structures
     • 9.3.3 Cascade-Form Structures
     • 9.3.4 Parallel-Form Structures
     • 9.3.5 Lattice and Lattice-Ladder Structures for IIR Systems
   • 9.4 Representation of Numbers
     • 9.4.1 Fixed-Point Representation of Numbers
     • 9.4.2 Binary Floating-Point Representation of Numbers
     • 9.4.3 Errors Resulting from Rounding and Truncation
   • 9.5 Quantization of Filter Coefficients
     • 9.5.1 Analysis of Sensitivity to Quantization of Filter Coefficients
     • 9.5.2 Quantization of Coefficients in FIR Filters
   • 9.6 Round-Off Effects in Digital Filters
     • 9.6.1 Limit-Cycle Oscillations in Recursive Systems
     • 9.6.2 Scaling to Prevent Overflow
     • 9.6.3 Statistical Characterization of Quantization Effects in Fixed-Point Realizations of Digital Filters
   • 9.7 Summary
   • Problems
   • Computer Problems
10. Design of Digital Filters
    • 10.1 General Considerations
      • 10.1.1 Causality and Its Implications
      • 10.1.2 Characteristics of Practical Frequency-Selective Filters
    • 10.2 Design of FIR Filters
      • 10.2.1 Symmetric and Antisymmetric FIR Filters
      • 10.2.2 Design of Linear-Phase FIR Filters Using Windows
      • 10.2.3 Design of Linear-Phase FIR Filters by the Frequency-Sampling Method
      • 10.2.4 Design of Optimum Equiripple Linear-Phase FIR Filters
      • 10.2.5 Design of FIR Differentiators
      • 10.2.6 Design of Hilbert Transformers
      • 10.2.7 Comparison of Design Methods for Linear-Phase FIR Filters
    • 10.3 Design of IIR Filters From Analog Filters
      • 10.3.1 IIR Filter Design by Approximation of Derivatives
      • 10.3.2 IIR Filter Design by Impulse Invariance
      • 10.3.3 IIR Filter Design by the Bilinear Transformation
      • 10.3.4 Characteristics of Commonly Used Analog Filters
      • 10.3.5 Some Examples of Digital Filter Designs Based on the Bilinear Transformation
    • 10.4 Frequency Transformations
      • 10.4.1 Frequency Transformations in the Analog Domain
      • 10.4.2 Frequency Transformations in the Digital Domain
    • 10.5 Summary
    • Problems
    • Computer Problems
11. Multirate Digital Signal Processing
    • 11.1 Introduction
    • 11.2 Decimation by a Factor D
    • 11.3 Interpolation by a Factor I
    • 11.4 Sampling Rate Conversion by a Rational Factor I /D
    • 11.5 Implementation of Sampling Rate Conversion
      • 11.5.1 Polyphase Filter Structures
      • 11.5.2 Interchange of Filters and Downsamplers/Upsamplers
      • 11.5.3 Sampling Rate Conversion with Cascaded Integrator Comb Filters
      • 11.5.4 Polyphase Structures for Decimation and Interpolation Filters
      • 11.5.5 Structures for Rational Sampling Rate Conversion
    • 11.6 Multistage Implementation of Sampling Rate Conversion
    • 11.7 Sampling Rate Conversion of Bandpass Signals
    • 11.8 Sampling Rate Conversion by an Arbitrary Factor
      • 11.8.1 Arbitrary Resampling with Polyphase Interpolators
      • 11.8.2 Arbitrary Resampling with Farrow Filter Structures
    • 11.9 Applications of Multirate Signal Processing
      • 11.9.1 Design of Phase Shifters
      • 11.9.2 Interfacing of Digital Systems with Different Sampling Rates
      • 11.9.3 Implementation of Narrowband Lowpass Filters
      • 11.9.4 Subband Coding of Speech Signals
    • 11.10 Summary
    • Problems
    • Computer Problems
12. Multirate Digital Filter Banks and Wavelets
    • 12.1 Multirate Digital Filter Banks
      • 12.1.1 DFT Filter Banks
      • 12.1.2 Polyphase Structure of the Uniform DFT Filter Bank
      • 12.1.3 An Alternative Structure of the Uniform DFT Filter Bank
    • 12.2 Two-Channel Quadrature Mirror Filter Bank
      • 12.2.1 Elimination of Aliasing
      • 12.2.2 Polyphase Structure of the QMF Bank
      • 12.2.3 Condition for Perfect Reconstruction
      • 12.2.4 Linear Phase FIR QMF Bank
      • 12.2.5 IIR QMF Bank
      • 12.2.6 Perfect Reconstruction in Two-Channel FIR QMF Bank
      • 12.2.7 Two-Channel Paraunitary QMF Bank
      • 12.2.8 Orthogonal and Biorthogonal Two-channel FIR Filter Banks
      • 12.2.9 Two-Channel QMF Banks in Subband Coding
    • 12.3 M-Channel Filter Banks
      • 12.3.1 Polyphase Structure for the M-Channel Filter Bank
      • 12.3.2 M-Channel Paraunitary Filter Banks
    • 12.4 Wavelets and Wavelet Transforms
      • 12.4.1 Ideal Bandpass Wavelet Decomposition
      • 12.4.2 Signal Spaces and Wavelets
      • 12.4.3 Multiresolution Analysis and Wavelets
      • 12.4.4 The Discrete Wavelet Transform
    • 12.5 From Wavelets to Filter Banks
      • 12.5.1 Dilation Equations
      • 12.5.2 Orthogonality Conditions
      • 12.5.3 Implications of Orthogonality and Dilation Equations
    • 12.6 From Filter Banks to Wavelets
    • 12.7 Regular Filters and Wavelets
    • 12.8 Summary
    • Problems
    • Computer Problems
13. Linear Prediction and Optimum Linear Filters
    • 13.1 Random Signals, Correlation Functions, and Power Spectra
      • 13.1.1 Random Processes
      • 13.1.2 Stationary Random Processes
      • 13.1.3 Statistical (Ensemble) Averages
      • 13.1.4 Statistical Averages for Joint Random Processes
      • 13.1.5 Power Density Spectrum
      • 13.1.6 Discrete-Time Random Signals
      • 13.1.7 Time Averages for a Discrete-Time Random Process
      • 13.1.8 Mean-Ergodic Process
      • 13.1.9 Correlation-Ergodic Processes
      • 13.1.10 Correlation Functions and Power Spectra for Random Input Signals to LTI Systems
    • 13.2 Innovations Representation of a Stationary Random Process
      • 13.2.1 Rational Power Spectra
      • 13.2.2 Relationships Between the Filter Parameters and the Autocorrelation Sequence
    • 13.3 Forward and Backward Linear Prediction
      • 13.3.1 Forward Linear Prediction
      • 13.3.2 Backward Linear Prediction
      • 13.3.3 The Optimum Reflection Coefficients for the Lattice Forward and Backward Predictors
      • 13.3.4 Relationship of an AR Process to Linear Prediction
    • 13.4 Solution of the Normal Equations
      • 13.4.1 The Levinson—Durbin Algorithm
    • 13.5 Properties of the Linear Prediction-Error Filters
    • 13.6 AR Lattice and ARMA Lattice-Ladder Filters
      • 13.6.1 AR Lattice Structure
      • 13.6.2 ARMA Processes and Lattice-Ladder Filters
    • 13.7 Wiener Filters for Filtering and Prediction
      • 13.7.1 FIR Wiener Filter
      • 13.7.2 Orthogonality Principle in Linear Mean-Square Estimation
      • 13.7.3 IIR Wiener Filter
      • 13.7.4 Noncausal Wiener Filter
    • 13.8 Summary
    • Problems
    • Computer Problems
14. Adaptive Filters
    • 14.1 Applications of Adaptive Filters
      • 14.1.1 System Identification or System Modeling
      • 14.1.2 Adaptive Channel Equalization
      • 14.1.3 Suppression of Narrowband Interference in a Wideband Signal
      • 14.1.4 Adaptive Line Enhancer
      • 14.1.5 Adaptive Noise Cancelling
      • 14.1.6 Adaptive Arrays
    • 14.2 Adaptive Direct-Form FIR Filters - The LMS Algorithm
      • 14.2.1 Minimum Mean-Square-Error Criterion
      • 14.2.2 The LMS Algorithm
      • 14.2.3 Related Stochastic Gradient Algorithms
      • 14.2.4 Properties of the LMS Algorithm
    • 14.3 Adaptive Direct-Form Filters - RLS Algorithms
      • 14.3.1 RLS Algorithm
      • 14.3.2 The LDU Factorization and Square-Root Algorithms
      • 14.3.3 Fast RLS Algorithms
      • 14.3.4 Properties of the Direct-Form RLS Algorithms
    • 14.4 Adaptive Lattice-Ladder Filters
      • 14.4.1 Recursive Least-Squares Lattice-Ladder Algorithms
      • 14.4.2 Other Lattice Algorithms
      • 14.4.3 Properties of Lattice-Ladder Algorithms
    • 14.5 Stability and Robustness of Adaptive Filter Algorithms
    • 14.6 Summary
    • Problems
    • Computer Problems
15. Power Spectrum Estimation
    • 15.1 Estimation of Spectra from Finite-Duration Observations of Signals
      • 15.1.1 Computation of the Energy Density Spectrum
      • 15.1.2 Estimation of the Autocorrelation and Power Spectrum of Random Signals: The Periodogram
      • 15.1.3 The Use of the DFT in Power Spectrum Estimation
    • 15.2 Nonparametric Methods for Power Spectrum Estimation
      • 15.2.1 The Bartlett Method: Averaging Periodograms
      • 15.2.2 The Welch Method: Averaging Modified Periodograms
      • 15.2.3 The Blackman and Tukey Method: Smoothing the Periodogram
      • 15.2.4 Performance Characteristics of Nonparametric Power Spectrum Estimators
      • 15.2.5 Computational Requirements of Nonparametric Power Spectrum Estimates
    • 15.3 Parametric Methods for Power Spectrum Estimation
      • 15.3.1 Relationships Between the Autocorrelation and the Model Parameters
      • 15.3.2 The Yule—Walker Method for the AR Model Parameters
      • 15.3.3 The Burg Method for the AR Model Parameters
      • 15.3.4 Unconstrained Least-Squares Method for the AR Model Parameters
      • 15.3.5 Sequential Estimation Methods for the AR Model Parameters
      • 15.3.6 Selection of AR Model Order
      • 15.3.7 MA Model for Power Spectrum Estimation
      • 15.3.8 ARMA Model for Power Spectrum Estimation
      • 15.3.9 Some Experimental Results
    • 15.4 ARMA Model Parameter Estimation
    • 15.5 Filter Bank Methods
      • 15.5.1 Filter Bank Realization of the Periodogram
      • 15.5.2 Minimum Variance Spectral Estimates
    • 15.6 Eigenanalysis Algorithms for Spectrum Estimation
      • 15.6.1 Pisarenko Harmonic Decomposition Method
      • 15.6.2 Eigen-decomposition of the Autocorrelation Matrix for Sinusoids in White Noise
      • 15.6.3 MUSIC Algorithm
      • 15.6.4 ESPRIT Algorithm
      • 15.6.5 Order Selection Criteria
      • 15.6.6 Experimental Results
    • 15.7 Summary
    • Problems
    • Computer Problems
      1. Random Number Generators
      2. Tables of Transition Coefficients for the Design of Linear-Phase FIR Filters

References and Bibliography

Answers to Selected Problems

Index