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 Title: Fast Algorithms for Volterra-Series-Based Nonlinear Adaptive Filters Author(s): Li, Xiaohui Doctoral Committee Chair(s): Jenkins, W. Kenneth Department / Program: Electrical Engineering Discipline: Electrical Engineering Degree Granting Institution: University of Illinois at Urbana-Champaign Degree: Ph.D. Genre: Dissertation Subject(s): Engineering, Electronics and Electrical Abstract: Two efficient algorithms for the second-order adaptive Volterra filter are developed in Chapter 2. By utilizing the special structure of the input correlation matrix of the Volterra filter the two algorithms essentially implement quasi-Newton algorithm with $O\lbrack {\rm N}\sp2\rbrack$ computational complexity which is equivalent to O (N) computational complexity of fast algorithms for linear adaptive filters. A new structure based on linear transformation and power normalization is introduced for third-order adaptive Volterra filters in Chapter 3. It is shown that the linear transformation and power normalization are very effective in improving the conditioning of third-order Volterra filter input. Because of the improved conditioning, the NLMS and data-reusing NLMS algorithms can achieve rapid convergence rate for third-order adaptive Volterra filter with very low computational complexity. The quasi-Newton algorithm is also applied to the third-order adaptive Volterra filter to achieve fast convergence rate. The preconditioned conjugate gradient algorithm is used to efficiently calculate the Kalman gain vector. A preconditioner, which is tailored to the structure of the correlation matrix of the third-order Volterra filter input, is developed for the preconditioned conjugate gradient algorithm. Chapter 4 presents an orthogonal-polynomial-based adaptive Volterra filtering algorithm. Polynomials that are statistically orthogonal for white Gaussian input are used to represent the Volterra series of finite order and memory. Because of the orthogonal property of the polynomial terms, the quasi-Newton algorithm is significantly simplified for adaptive Volterra filter. The frequency domain block LMS algorithms for linear and nonlinear adaptive filters are discussed in Chapter 5. The main focus of the chapter is on analyzing the fundamental difference between the constrained and the unconstrained frequency domain block LMS algorithms for linear and nonlinear adaptive filters. In Chapter 6, the adaptive algorithms developed through the previous chapters are applied to echo cancellation for a 256-QAM full-duplex digital transmission system and to acoustic echo cancellation. The computer simulation results and their performance comparisons are presented in this chapter. Issue Date: 1998 Type: Text Language: English Description: 136 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1998. URI: http://hdl.handle.net/2142/81249 Other Identifier(s): (MiAaPQ)AAI9904526 Date Available in IDEALS: 2015-09-25 Date Deposited: 1998
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