By Bernard Widrow
A complete and sensible remedy of adaptive sign processing that includes widespread use of examples.
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Extra info for Adaptive Signal Processing
Matrix H'(k)W(k)H(k) is said to be nonsingular if it has an inverse satisfying [H1 (k)W(k)H(k)r 1[H 1 (k)W(k)H(k)] = [H'(k)W(k)H(k)][H'(k)W(k)H(k)r 1 =I IfW(k) is positive definite, then it can be written uniquely as W(k) = L'(k)L(k), where L(k) is a lower triangular matrix with positive diagonal elements. , is of maximum rank, then rank [H(k)], because A'(k)A(k) is nonsingular. Finally, rank [L(k)H(k)] L(k) is nonsingular. Consequently, if H(k) is of maximum rank, then A'(k)A(k) is nonsingular, so [A'(k)A(k)]- 1 = [H'(k)W(k)H(k)]- 1 exists.
He is now credited with being one of the founders of non-Euclidean geometry). For discussions of an interesting feud between Gauss and Legendre over priority to the method of least squares, see Sorenson (1970). Gauss died at 78 on February 23, 1855. " NUMBER OF MEASUREMENTS Suppose that e contains n parameters and Z(k) contains N measurements. If N < n, we have fewer measurements than unknowns and (3-1) is an underdetermined system of equations that does not lead to unique values for 01, fJ2 , ••• , fJ,.
The linear prediction problem is analogous to: (a) estimating impulse response coefficients (b) deconvolution (c) estimating AR coefficients 7. The mathematical model that underlies the reflection seismology convolutional model is the: (a) lossy wave equation (b) heat equation (c) lossless wave equation 8. "Past" measurements always: (a) lie to the right of present time (b) lie to the left of present time (c) include the measurement made at the present time 9. An estimator, as distinct from an estimate, is: (a) a filter structure (b) a model (c) a numerical value of an estimate 10.
Adaptive Signal Processing by Bernard Widrow