Linear Algebra for Signal ProcessingAdam Bojanczyk, George Cybenko Signal processing applications have burgeoned in the past decade. During the same time, signal processing techniques have matured rapidly and now include tools from many areas of mathematics, computer science, physics, and engineering. This trend will continue as many new signal processing applications are opening up in consumer products and communications systems. In particular, signal processing has been making increasingly sophisticated use of linear algebra on both theoretical and algorithmic fronts. This volume gives particular emphasis to exposing broader contexts of the signal processing problems so that the impact of algorithms and hardware can be better understood; it brings together the writings of signal processing engineers, computer engineers, and applied linear algebraists in an exchange of problems, theories, and techniques. This volume will be of interest to both applied mathematicians and engineers. |
Contents
Preface | 1 |
Structured condition numbers for linear matrix structures | 17 |
Application to wavelets | 51 |
Wavelets filter banks and arbitrary tilings of the timefrequency plane | 83 |
Systolic algorithms for adaptive signal processing | 125 |
Adaptive algorithms for blind channel equalization | 139 |
Squareroot algorithms for structured matrices interpolation | 153 |
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Common terms and phrases
algorithm analysis Applications array basis functions blind equalization canonical correlations cascade Cauchy matrices Ck+1 coefficients column compute consider construction continuous-time convergence COROLLARY data sequence defined denote diagonal dilation equation discrete-time displacement rank displacement structure Editors eigenvalues entries example factor Figure filter banks frequency G₁ given Go(z H₁ Hence Ho(z IEEE Trans impulse response interpolation problem inverse iteration joint spectral radius Kailath Kalman filter Koltracht least squares LEMMA Linear Algebra linear phase Mathematics matrix pair multidimensional nonsingular obtained operator orthogonal orthogonal matrix orthonormal basis perfect reconstruction perturbation Proof QR decomposition QR update recursive result row vectors satisfies scaling function Schur Schur complement Section SIAM Signal Proc Signal Processing solution span{B spectral radius structured matrices subspace SVD updating systolic systolic array T₁ Theorem 3.1 Theory tiling time-variant tion Toeplitz matrices Töplitz triangular Volume wavelet packet zero ακ