Digital Signal Processing

<div class="c-un-numbered-headers-and-contents-list__container"> <ol> <li><strong>Introduction</strong> <ul> <li>1.1 Signals, Systems, and Signal Processing <ul> <li>1.1.1 Basic Elements of a Digital Signal Processing System</li> <li>1.1.2 Advantages of Digital over Analog Signal Processing</li> </ul></li> <li>1.2 Classification of Signals <ul> <li>1.2.1 Multichannel and Multidimensional Signals</li> <li>1.2.2 Continuous-Time Versus Discrete-Time Signals</li> <li>1.2.3 Continuous-Valued Versus Discrete-Valued Signals</li> <li>1.2.4 Deterministic Versus Random Signals</li> </ul></li> <li>1.3 Summary</li> </ul> <ul> <li>Problems</li> </ul></li> <li><strong>Discrete-Time Signals and Systems</strong> <ul> <li>2.1 Discrete-Time Signals <ul> <li>2.1.1 Some Elementary Discrete-Time Signals</li> <li>2.1.2 Classification of Discrete-Time Signals</li> <li>2.1.3 Simple Manipulations of Discrete-Time Signals</li> </ul></li> <li>2.2 Discrete-Time Systems <ul> <li>2.2.1 Input-Output Description of Systems</li> <li>2.2.2 Block Diagram Representation of Discrete-Time Systems</li> <li>2.2.3 Classification of Discrete-Time Systems</li> <li>2.2.4 Interconnection of Discrete-Time Systems</li> </ul></li> <li>2.3 Analysis of Discrete-Time Linear Time-Invariant Systems <ul> <li>2.3.1 Techniques for the Analysis of Linear Systems</li> <li>2.3.2 Resolution of a Discrete-Time Signal into Impulses</li> <li>2.3.3 Response of LTI Systems to Arbitrary Inputs: The Convolution Sum</li> <li>2.3.4 Properties of Convolution and the Interconnection of LTI Systems</li> <li>2.3.5 Causal Linear Time-Invariant Systems</li> <li>2.3.6 Stability of Linear Time-Invariant Systems</li> <li>2.3.7 Systems with Finite-Duration and Infinite-Duration Impulse Response</li> </ul></li> <li>2.4 Discrete-Time Systems Described by Difference Equations <ul> <li>2.4.1 Recursive and Nonrecursive Discrete-Time Systems</li> <li>2.4.2 Linear Time-Invariant Systems Characterized by Constant-Coefficient Difference Equations</li> <li>2.4.3 Application of LTI Systems for Signal Smoothing</li> </ul></li> <li>2.5 Implementation of Discrete-Time Systems <ul> <li>2.5.1 Structures for the Realization of Linear Time-Invariant Systems</li> <li>2.5.2 Recursive and Nonrecursive Realizations of FIR Systems</li> </ul></li> <li>2.6 Correlation of Discrete-Time Signals <ul> <li>2.6.1 Crosscorrelation and Autocorrelation Sequences</li> <li>2.6.2 Properties of the Autocorrelation and Crosscorrelation Sequences</li> <li>2.6.3 Correlation of Periodic Sequences</li> <li>2.6.4 Input-Output Correlation Sequences</li> </ul></li> <li>2.7 Summary</li> </ul> <ul> <li>Problems</li> <li>Computer Problems</li> </ul></li> <li><strong>The z-Transform and Its Application to the Analysis of LTI Systems</strong> <ul> <li>3.1 The z-Transform <ul> <li>3.1.1 The Direct z-Transform</li> <li>3.1.2 The Inverse z-Transform</li> </ul></li> <li>3.2 Properties of the z-Transform</li> <li>3.3 Rational z-Transforms <ul> <li>3.3.1 Poles and Zeros</li> <li>3.3.2 Pole Location and Time-Domain Behavior for Causal Signals</li> <li>3.3.3 The System Function of a Linear Time-Invariant System</li> </ul></li> <li>3.4 Inversion of the z-Transform <ul> <li>3.4.1 The Inverse z-Transform by Contour Integration</li> <li>3.4.2 The Inverse z-Transform by Power Series Expansion</li> <li>3.4.3 The Inverse z-Transform by Partial-Fraction Expansion</li> <li>3.4.4 Decomposition of Rational z-Transforms</li> </ul></li> <li>3.5 Analysis of Linear Time-Invariant Systems in the z-Domain <ul> <li>3.5.1 Response of Systems with Rational System Functions</li> <li>3.5.2 Transient and Steady-State Responses</li> <li>3.5.3 Causality and Stability</li> <li>3.5.4 Pole—Zero Cancellations</li> <li>3.5.5 Multiple-Order Poles and Stability</li> <li>3.5.6 Stability of Second-Order Systems</li> </ul></li> <li>3.6 The One-sided z-Transform <ul> <li>3.6.1 Definition and Properties</li> <li>3.6.2 Solution of Difference Equations</li> <li>3.6.3 Response of Pole—Zero Systems with Nonzero Initial Conditions</li> </ul></li> <li>3.7 Summary</li> </ul> <ul> <li>Problems</li> <li>Computer Problems</li> </ul></li> <li><strong>Frequency Analysis of Signals</strong> <ul> <li>4.1 The Concept of Frequency in Continuous-Time and Discrete-Time Signals <ul> <li>4.1.1 Continuous-Time Sinusoidal Signals</li> <li>4.1.2 Discrete-Time Sinusoidal Signals</li> <li>4.1.3 Harmonically Related Complex Exponentials</li> <li>4.1.4 Sampling of Analog Signals</li> <li>4.1.5 The Sampling Theorem</li> </ul></li> <li>4.2 Frequency Analysis of Continuous-Time Signals <ul> <li>4.2.1 The Fourier Series for Continuous-Time Periodic Signals</li> <li>4.2.2 Power Density Spectrum of Periodic Signals</li> <li>4.2.3 The Fourier Transform for Continuous-Time Aperiodic Signals</li> <li>4.2.4 Energy Density Spectrum of Aperiodic Signals</li> </ul></li> <li>4.3 Frequency Analysis of Discrete-Time Signals <ul> <li>4.3.1 The Fourier Series for Discrete-Time Periodic Signals</li> <li>4.3.2 Power Density Spectrum of Periodic Signals</li> <li>4.3.3 The Fourier Transform of Discrete-Time Aperiodic Signals</li> <li>4.3.4 Convergence of the Fourier Transform</li> <li>4.3.5 Energy Density Spectrum of Aperiodic Signals</li> <li>4.3.6 Relationship of the Fourier Transform to the z-Transform</li> <li>4.3.7 The Cepstrum</li> <li>4.3.8 The Fourier Transform of Signals with Poles on the Unit Circle</li> <li>4.3.9 Frequency-Domain Classification of Signals: The Concept of Bandwidth</li> <li>4.3.10 The Frequency Ranges of Some Natural Signals</li> </ul></li> <li>4.4 Frequency-Domain and Time-Domain Signal Properties</li> <li>4.5 Properties of the Fourier Transform for Discrete-Time Signals <ul> <li>4.5.1 Symmetry Properties of the Fourier Transform</li> <li>4.5.2 Fourier Transform Theorems and Properties</li> </ul></li> <li>4.6 Summary</li> </ul> <ul> <li>Problems</li> <li>Computer Problems</li> </ul></li> <li><strong>Frequency-Domain Analysis of LTI Systems</strong> <ul> <li>5.1 Frequency-Domain Characteristics of Linear Time-Invariant Systems <ul> <li>5.1.1 Response to Complex Exponential and Sinusoidal Signals: The Frequency Response Function</li> <li>5.1.2 Steady-State and Transient Response to Sinusoidal Input Signals</li> <li>5.1.3 Steady-State Response to Periodic Input Signals</li> <li>5.1.4 Steady-State Response to Aperiodic Input Signals</li> </ul></li> <li>5.2 Frequency Response of LTI Systems <ul> <li>5.2.1 Frequency Response of a System with a Rational System Function</li> <li>5.2.2 Computation of the Frequency Response Function</li> </ul></li> <li>5.3 Correlation Functions and Spectra at the Output of LTI Systems</li> <li>5.4 Linear Time-Invariant Systems as Frequency-Selective Filters <ul> <li>5.4.1 Ideal Filter Characteristics</li> <li>5.4.2 Lowpass, Highpass, and Bandpass Filters</li> <li>5.4.3 Digital Resonators</li> <li>5.4.4 Notch Filters</li> <li>5.4.5 Comb Filters</li> <li>5.4.6 Reverberation Filters</li> <li>5.4.7 All-Pass Filters</li> <li>5.4.8 Digital Sinusoidal Oscillators</li> </ul></li> <li>5.5 Inverse Systems and Deconvolution <ul> <li>5.5.1 Invertibility of Linear Time-Invariant Systems</li> <li>5.5.2 Minimum-Phase, Maximum-Phase, and Mixed-Phase Systems</li> <li>5.5.3 System Identification and Deconvolution</li> <li>5.5.4 Homomorphic Deconvolution</li> </ul></li> <li>5.6 Summary</li> </ul> <ul> <li>Problems</li> <li>Computer Problems</li> </ul></li> <li><strong>Sampling and Reconstruction of Signals</strong> <ul> <li>6.1 Ideal Sampling and Reconstruction of Continuous-Time Signals</li> <li>6.2 Discrete-Time Processing of Continuous-Time Signals</li> <li>6.3 Sampling and Reconstruction of Continuous-Time Bandpass Signals <ul> <li>6.3.1 Uniform or First-Order Sampling</li> <li>6.3.2 Interleaved or Nonuniform Second-Order Sampling</li> <li>6.3.3 Bandpass Signal Representations</li> <li>6.3.4 Sampling Using Bandpass Signal Representations</li> </ul></li> <li>6.4 Sampling of Discrete-Time Signals <ul> <li>6.4.1 Sampling and Interpolation of Discrete-Time Signals</li> <li>6.4.2 Representation and Sampling of Bandpass Discrete-Time Signals</li> </ul></li> <li>6.5 Analog-to-Digital and Digital-to-Analog Converters <ul> <li>6.5.1 Analog-to-Digital Converters</li> <li>6.5.2 Quantization and Coding</li> <li>6.5.3 Analysis of Quantization Errors</li> <li>6.5.4 Digital-to-Analog Converters</li> </ul></li> <li>6.6 Oversampling A/D and D/A Converters <ul> <li>6.6.1 Oversampling A/D Converters</li> <li>6.6.2 Oversampling D/A Converters</li> </ul></li> <li>6.7 Summary</li> </ul> <ul> <li>Problems</li> <li>Computer Problems</li> </ul></li> <li><strong>The Discrete Fourier Transform: Its Properties and Applications</strong> <ul> <li>7.1 Frequency-Domain Sampling: The Discrete Fourier Transform <ul> <li>7.1.1 Frequency-Domain Sampling and Reconstruction of Discrete-Time Signals</li> <li>7.1.2 The Discrete Fourier Transform (DFT)</li> <li>7.1.3 The DFT as a Linear Transformation</li> <li>7.1.4 Relationship of the DFT to Other Transforms</li> </ul></li> <li>7.2 Properties of the DFT <ul> <li>7.2.1 Periodicity, Linearity, and Symmetry Properties</li> <li>7.2.2 Multiplication of Two DFTs and Circular Convolution</li> <li>7.2.3 Additional DFT Properties</li> </ul></li> <li>7.3 Linear Filtering Methods Based on the DFT <ul> <li>7.3.1 Use of the DFT in Linear Filtering</li> <li>7.3.2 Filtering of Long Data Sequences</li> </ul></li> <li>7.4 Frequency Analysis of Signals Using the DFT</li> <li>7.5 The Short-Time Fourier Transform</li> <li>7.6 The Discrete Cosine Transform <ul> <li>7.6.1 Forward DCT</li> <li>7.6.2 Inverse DCT</li> <li>7.6.3 DCT as an Orthogonal Transform</li> </ul></li> <li>7.7 Summary</li> </ul> <ul> <li>Problems</li> <li>Computer Problems</li> </ul></li> <li><strong>Efficient Computation of the DFT: Fast Fourier Transform Algorithms</strong> <ul> <li>8.1 Efficient Computation of the DFT: FFT Algorithms <ul> <li>8.1.1 Direct Computation of the DFT</li> <li>8.1.2 Divide-and-Conquer Approach to Computation of the DFT</li> <li>8.1.3 Radix-2 FFT Algorithms</li> <li>8.1.4 Radix-4 FFT Algorithms</li> <li>8.1.5 Split-Radix FFT Algorithms</li> <li>8.1.6 Implementation of FFT Algorithms</li> <li>8.1.7 Sparse FFT Algorithm</li> </ul></li> <li>8.2 Applications of FFT Algorithms <ul> <li>8.2.1 Efficient Computation of the DFT of Two Real Sequences</li> <li>8.2.2 Efficient Computation of the DFT of a 2N-Point Real Sequence</li> <li>8.2.3 Use of the FFT Algorithm in Linear Filtering and Correlation</li> </ul></li> <li>8.3 A Linear Filtering Approach to Computation of the DFT <ul> <li>8.3.1 The Goertzel Algorithm</li> <li>8.3.2 The Chirp-z Transform Algorithm</li> </ul></li> <li>8.4 Quantization Effects in the Computation of the DFT <ul> <li>8.4.1 Quantization Errors in the Direct Computation of the DFT</li> <li>8.4.2 Quantization Errors in FFT Algorithms</li> </ul></li> <li>8.5 Summary</li> </ul> <ul> <li>Problems</li> <li>Computer Problems</li> </ul></li> <li><strong>Implementation of Discrete-Time Systems</strong> <ul> <li>9.1 Structures for the Realization of Discrete-Time Systems</li> <li>9.2 Structures for FIR Systems <ul> <li>9.2.1 Direct-Form Structure</li> <li>9.2.2 Cascade-Form Structures</li> <li>9.2.3 Frequency-Sampling Structures</li> <li>9.2.4 Lattice Structure</li> </ul></li> <li>9.3 Structures for IIR Systems <ul> <li>9.3.1 Direct-Form Structures</li> <li>9.3.2 Signal Flow Graphs and Transposed Structures</li> <li>9.3.3 Cascade-Form Structures</li> <li>9.3.4 Parallel-Form Structures</li> <li>9.3.5 Lattice and Lattice-Ladder Structures for IIR Systems</li> </ul></li> <li>9.4 Representation of Numbers <ul> <li>9.4.1 Fixed-Point Representation of Numbers</li> <li>9.4.2 Binary Floating-Point Representation of Numbers</li> <li>9.4.3 Errors Resulting from Rounding and Truncation</li> </ul></li> <li>9.5 Quantization of Filter Coefficients <ul> <li>9.5.1 Analysis of Sensitivity to Quantization of Filter Coefficients</li> <li>9.5.2 Quantization of Coefficients in FIR Filters</li> </ul></li> <li>9.6 Round-Off Effects in Digital Filters <ul> <li>9.6.1 Limit-Cycle Oscillations in Recursive Systems</li> <li>9.6.2 Scaling to Prevent Overflow</li> <li>9.6.3 Statistical Characterization of Quantization Effects in Fixed-Point Realizations of Digital Filters</li> </ul></li> <li>9.7 Summary</li> </ul> <ul> <li>Problems</li> <li>Computer Problems</li> </ul></li> <li><strong>Design of Digital Filters</strong> <ul> <li>10.1 General Considerations <ul> <li>10.1.1 Causality and Its Implications</li> <li>10.1.2 Characteristics of Practical Frequency-Selective Filters</li> </ul></li> <li>10.2 Design of FIR Filters <ul> <li>10.2.1 Symmetric and Antisymmetric FIR Filters</li> <li>10.2.2 Design of Linear-Phase FIR Filters Using Windows</li> <li>10.2.3 Design of Linear-Phase FIR Filters by the Frequency-Sampling Method</li> <li>10.2.4 Design of Optimum Equiripple Linear-Phase FIR Filters</li> <li>10.2.5 Design of FIR Differentiators</li> <li>10.2.6 Design of Hilbert Transformers</li> <li>10.2.7 Comparison of Design Methods for Linear-Phase FIR Filters</li> </ul></li> <li>10.3 Design of IIR Filters From Analog Filters <ul> <li>10.3.1 IIR Filter Design by Approximation of Derivatives</li> <li>10.3.2 IIR Filter Design by Impulse Invariance</li> <li>10.3.3 IIR Filter Design by the Bilinear Transformation</li> <li>10.3.4 Characteristics of Commonly Used Analog Filters</li> <li>10.3.5 Some Examples of Digital Filter Designs Based on the Bilinear Transformation</li> </ul></li> <li>10.4 Frequency Transformations <ul> <li>10.4.1 Frequency Transformations in the Analog Domain</li> <li>10.4.2 Frequency Transformations in the Digital Domain</li> </ul></li> <li>10.5 Summary</li> </ul> <ul> <li>Problems</li> <li>Computer Problems</li> </ul></li> <li><strong>Multirate Digital Signal Processing</strong> <ul> <li>11.1 Introduction</li> <li>11.2 Decimation by a Factor D</li> <li>11.3 Interpolation by a Factor I</li> <li>11.4 Sampling Rate Conversion by a Rational Factor I /D</li> <li>11.5 Implementation of Sampling Rate Conversion <ul> <li>11.5.1 Polyphase Filter Structures</li> <li>11.5.2 Interchange of Filters and Downsamplers/Upsamplers</li> <li>11.5.3 Sampling Rate Conversion with Cascaded Integrator Comb Filters</li> <li>11.5.4 Polyphase Structures for Decimation and Interpolation Filters</li> <li>11.5.5 Structures for Rational Sampling Rate Conversion</li> </ul></li> <li>11.6 Multistage Implementation of Sampling Rate Conversion</li> <li>11.7 Sampling Rate Conversion of Bandpass Signals</li> <li>11.8 Sampling Rate Conversion by an Arbitrary Factor <ul> <li>11.8.1 Arbitrary Resampling with Polyphase Interpolators</li> <li>11.8.2 Arbitrary Resampling with Farrow Filter Structures</li> </ul></li> <li>11.9 Applications of Multirate Signal Processing <ul> <li>11.9.1 Design of Phase Shifters</li> <li>11.9.2 Interfacing of Digital Systems with Different Sampling Rates</li> <li>11.9.3 Implementation of Narrowband Lowpass Filters</li> <li>11.9.4 Subband Coding of Speech Signals</li> </ul></li> <li>11.10 Summary</li> </ul> <ul> <li>Problems</li> <li>Computer Problems</li> </ul></li> <li><strong>Multirate Digital Filter Banks and Wavelets</strong> <ul> <li>12.1 Multirate Digital Filter Banks <ul> <li>12.1.1 DFT Filter Banks</li> <li>12.1.2 Polyphase Structure of the Uniform DFT Filter Bank</li> <li>12.1.3 An Alternative Structure of the Uniform DFT Filter Bank</li> </ul></li> <li>12.2 Two-Channel Quadrature Mirror Filter Bank <ul> <li>12.2.1 Elimination of Aliasing</li> <li>12.2.2 Polyphase Structure of the QMF Bank</li> <li>12.2.3 Condition for Perfect Reconstruction</li> <li>12.2.4 Linear Phase FIR QMF Bank</li> <li>12.2.5 IIR QMF Bank</li> <li>12.2.6 Perfect Reconstruction in Two-Channel FIR QMF Bank</li> <li>12.2.7 Two-Channel Paraunitary QMF Bank</li> <li>12.2.8 Orthogonal and Biorthogonal Two-channel FIR Filter Banks</li> <li>12.2.9 Two-Channel QMF Banks in Subband Coding</li> </ul></li> <li>12.3 M-Channel Filter Banks <ul> <li>12.3.1 Polyphase Structure for the M-Channel Filter Bank</li> <li>12.3.2 M-Channel Paraunitary Filter Banks</li> </ul></li> <li>12.4 Wavelets and Wavelet Transforms <ul> <li>12.4.1 Ideal Bandpass Wavelet Decomposition</li> <li>12.4.2 Signal Spaces and Wavelets</li> <li>12.4.3 Multiresolution Analysis and Wavelets</li> <li>12.4.4 The Discrete Wavelet Transform</li> </ul></li> <li>12.5 From Wavelets to Filter Banks <ul> <li>12.5.1 Dilation Equations</li> <li>12.5.2 Orthogonality Conditions</li> <li>12.5.3 Implications of Orthogonality and Dilation Equations</li> </ul></li> <li>12.6 From Filter Banks to Wavelets</li> <li>12.7 Regular Filters and Wavelets</li> <li>12.8 Summary</li> </ul> <ul> <li>Problems</li> <li>Computer Problems</li> </ul></li> <li><strong>Linear Prediction and Optimum Linear Filters</strong> <ul> <li>13.1 Random Signals, Correlation Functions, and Power Spectra <ul> <li>13.1.1 Random Processes</li> <li>13.1.2 Stationary Random Processes</li> <li>13.1.3 Statistical (Ensemble) Averages</li> <li>13.1.4 Statistical Averages for Joint Random Processes</li> <li>13.1.5 Power Density Spectrum</li> <li>13.1.6 Discrete-Time Random Signals</li> <li>13.1.7 Time Averages for a Discrete-Time Random Process</li> <li>13.1.8 Mean-Ergodic Process</li> <li>13.1.9 Correlation-Ergodic Processes</li> <li>13.1.10 Correlation Functions and Power Spectra for Random Input Signals to LTI Systems</li> </ul></li> <li>13.2 Innovations Representation of a Stationary Random Process <ul> <li>13.2.1 Rational Power Spectra</li> <li>13.2.2 Relationships Between the Filter Parameters and the Autocorrelation Sequence</li> </ul></li> <li>13.3 Forward and Backward Linear Prediction <ul> <li>13.3.1 Forward Linear Prediction</li> <li>13.3.2 Backward Linear Prediction</li> <li>13.3.3 The Optimum Reflection Coefficients for the Lattice Forward and Backward Predictors</li> <li>13.3.4 Relationship of an AR Process to Linear Prediction</li> </ul></li> <li>13.4 Solution of the Normal Equations <ul> <li>13.4.1 The Levinson—Durbin Algorithm</li> </ul></li> <li>13.5 Properties of the Linear Prediction-Error Filters</li> <li>13.6 AR Lattice and ARMA Lattice-Ladder Filters <ul> <li>13.6.1 AR Lattice Structure</li> <li>13.6.2 ARMA Processes and Lattice-Ladder Filters</li> </ul></li> <li>13.7 Wiener Filters for Filtering and Prediction <ul> <li>13.7.1 FIR Wiener Filter</li> <li>13.7.2 Orthogonality Principle in Linear Mean-Square Estimation</li> <li>13.7.3 IIR Wiener Filter</li> <li>13.7.4 Noncausal Wiener Filter</li> </ul></li> <li>13.8 Summary</li> </ul> <ul> <li>Problems</li> <li>Computer Problems</li> </ul></li> <li><strong>Adaptive Filters</strong> <ul> <li>14.1 Applications of Adaptive Filters <ul> <li>14.1.1 System Identification or System Modeling</li> <li>14.1.2 Adaptive Channel Equalization</li> <li>14.1.3 Suppression of Narrowband Interference in a Wideband Signal</li> <li>14.1.4 Adaptive Line Enhancer</li> <li>14.1.5 Adaptive Noise Cancelling</li> <li>14.1.6 Adaptive Arrays</li> </ul></li> <li>14.2 Adaptive Direct-Form FIR Filters - The LMS Algorithm <ul> <li>14.2.1 Minimum Mean-Square-Error Criterion</li> <li>14.2.2 The LMS Algorithm</li> <li>14.2.3 Related Stochastic Gradient Algorithms</li> <li>14.2.4 Properties of the LMS Algorithm</li> </ul></li> <li>14.3 Adaptive Direct-Form Filters - RLS Algorithms <ul> <li>14.3.1 RLS Algorithm</li> <li>14.3.2 The LDU Factorization and Square-Root Algorithms</li> <li>14.3.3 Fast RLS Algorithms</li> <li>14.3.4 Properties of the Direct-Form RLS Algorithms</li> </ul></li> <li>14.4 Adaptive Lattice-Ladder Filters <ul> <li>14.4.1 Recursive Least-Squares Lattice-Ladder Algorithms</li> <li>14.4.2 Other Lattice Algorithms</li> <li>14.4.3 Properties of Lattice-Ladder Algorithms</li> </ul></li> <li>14.5 Stability and Robustness of Adaptive Filter Algorithms</li> <li>14.6 Summary</li> </ul> <ul> <li>Problems</li> <li>Computer Problems</li> </ul></li> <li><strong>Power Spectrum Estimation</strong> <ul> <li>15.1 Estimation of Spectra from Finite-Duration Observations of Signals <ul> <li>15.1.1 Computation of the Energy Density Spectrum</li> <li>15.1.2 Estimation of the Autocorrelation and Power Spectrum of Random Signals: The Periodogram</li> <li>15.1.3 The Use of the DFT in Power Spectrum Estimation</li> </ul></li> <li>15.2 Nonparametric Methods for Power Spectrum Estimation <ul> <li>15.2.1 The Bartlett Method: Averaging Periodograms</li> <li>15.2.2 The Welch Method: Averaging Modified Periodograms</li> <li>15.2.3 The Blackman and Tukey Method: Smoothing the Periodogram</li> <li>15.2.4 Performance Characteristics of Nonparametric Power Spectrum Estimators</li> <li>15.2.5 Computational Requirements of Nonparametric Power Spectrum Estimates</li> </ul></li> <li>15.3 Parametric Methods for Power Spectrum Estimation <ul> <li>15.3.1 Relationships Between the Autocorrelation and the Model Parameters</li> <li>15.3.2 The Yule—Walker Method for the AR Model Parameters</li> <li>15.3.3 The Burg Method for the AR Model Parameters</li> <li>15.3.4 Unconstrained Least-Squares Method for the AR Model Parameters</li> <li>15.3.5 Sequential Estimation Methods for the AR Model Parameters</li> <li>15.3.6 Selection of AR Model Order</li> <li>15.3.7 MA Model for Power Spectrum Estimation</li> <li>15.3.8 ARMA Model for Power Spectrum Estimation</li> <li>15.3.9 Some Experimental Results</li> </ul></li> <li>15.4 ARMA Model Parameter Estimation</li> <li>15.5 Filter Bank Methods <ul> <li>15.5.1 Filter Bank Realization of the Periodogram</li> <li>15.5.2 Minimum Variance Spectral Estimates</li> </ul></li> <li>15.6 Eigenanalysis Algorithms for Spectrum Estimation <ul> <li>15.6.1 Pisarenko Harmonic Decomposition Method</li> <li>15.6.2 Eigen-decomposition of the Autocorrelation Matrix for Sinusoids in White Noise</li> <li>15.6.3 MUSIC Algorithm</li> <li>15.6.4 ESPRIT Algorithm</li> <li>15.6.5 Order Selection Criteria</li> <li>15.6.6 Experimental Results</li> </ul></li> <li>15.7 Summary</li> </ul> <ul> <li>Problems</li> <li>Computer Problems <ol type="A"> <li>Random Number Generators</li> <li>Tables of Transition Coefficients for the Design of Linear-Phase FIR Filters</li> </ol></li> </ul></li> </ol> <h4 class="5">References and Bibliography</h4> <h4 class="5">Answers to Selected Problems</h4> <h4 class="5">Index</h4> </div>