Algorithms for Statistical Signal Processing

1. Introduction.


Characterization of Signals. Characterization of Linear Time-Invariant Systems. Sampling of Signals. Linear Filtering Methods Based on the DFT. The Cepstrum. Summary and References. Problems.



2. Algorithms for Convolution and DFT.


Modulo Polynomials. Circular Convolution as Polynomial Multiplication mod un- 1. A Continued Fraction of Polynomials. Chinese Remainder Theorem for Polynomials. Algorithms for Short Circular Convolutions. How We Count Multiplications. Cyclotomic Polynomials. Elementary Number Theory. Convolution Length and Dimension. The DFT as a Circular Convolution. Winograd's DFT Algorithm. Number-Theoretic Analogy of DFT. Number-Theoretic Transform. Split-Radix FFT. Autogen Technique. Summary and References. Problems.



3. Linear Prediction and Optimum Linear Filters.


Innovations Representation of a Stationary Random Process. Forward and Backward Linear Prediction. Solution of the Normal Equations. Properties of the Linear Prediction-Error Filters. AR Lattice and ARMA Lattice-Ladder Filters. Wiener Filters for Filtering and Prediction. Summary and References. Problems.



4. Least-Squares Methods for System Modeling and Filter Design.


System Modeling and Identification. Lease-Squares Filter Design for Prediction and Deconvolution. Solution of Least-Squares Estimation Problems. Summary and References. Problems.



5. Adaptive Filters.


Applications of Adaptive Filters. Adaptive Direct-Form FIR Filters. Adaptive Lattice-Ladder Filters. Summary and References. Problems.



6. Recursive Least-Squares Algorithms for Array Signal Processing.


QR Decomposition for Least-Squares Estimation. Gram-Schmidt Orthogonalization for Least-Squares Estimation. Givens Algorithm for Time-Recursive Least-Squares Estimation. Recursive Least-Squares Estimation Based on the Householder Transformation. Order-Recursive Least-Squares Estimation Algorithms. Summary and References. Problems.



7. QRD-Based Fast Adaptive Filter Algorithms.


Background. QRD Lattice. Multichannel Lattice. Fast QR Algorithm. Multichannel Fast QR Algorithm. Summary and References. Problems.



8. Power Spectrum Estimation.


Estimation of Spectra from Finite-Duration Observations of Signals. Nonparametric Methods for Power Spectrum Estimation. Parametric Methods for Power Spectrum Estimation. Minimum-Variance Spectral Estimation. Eigenanalysis Algorithms for Spectrum Estimation. Summary and References. Problems.



9. Signal Analysis with Higher-Order Spectra.


Use of Higher-Order Spectra in Signal Processing. Definition and Properties of Higher-Order Spectra. Conventional Estimators for Higher-Order Spectra. Parametric Methods for Higher-Order Spectrum Estimation. Cepstra of Higher-Order Spectra. Phase and Magnitude Retrieval from the Bispectrum. Summary and References. Problems.



References.


Index.