Adaptive Signal Processing: Theory and Applications by Thomas S. Alexander

By Thomas S. Alexander

The production of the textual content rather started in 1976 with the writer being concerned with a bunch of researchers at Stanford collage and the Naval Ocean structures heart, San Diego. at the moment, adaptive ideas have been extra laboratory (and psychological) curiosities than the permitted and pervasive different types of sign processing that they have got turn into. Over the lasl 10 years, adaptive filters became commonplace parts in telephony, info communications, and sign detection and monitoring platforms. Their use and patron reputation will certainly merely bring up sooner or later. The mathematical rules underlying adaptive sign processing have been firstly interesting and have been my first event in seeing utilized arithmetic paintings for a paycheck. seeing that that point, the appliance of much more complicated mathematical suggestions have saved the world of adaptive sign processing as interesting as these preliminary days. The textual content seeks to be a bridge among the open literature within the expert journals, that's often rather focused, concise, and complicated, and the graduate school room and examine atmosphere the place underlying rules are frequently extra important.

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Another tutorial work concerning gradient-based methods is that by Sakrison [6). Much of the analytical work done in gradient based adaptive filtering (such as the LMS algorithm) also contains analyses of the method of steepest descent for comparison purposes. The text by Wid row and Stearns [20] covers many aspects of gradient-based methods at the introductory level. Also at the introductory level are three excellent works in this area by Widrow [7], Wid row and McCool [8], and Treichler [9], and at the somewhat more advanced level, the paper by Senne and Horowitz [10] is very explanatory.

11. M. L. Marple, "Spectrum Analysis- A Modern Perspective," Proceeding of the IEEE, vol. 69, pp. 1380- 1419, November 1981. 12. 1. Makhoul, "Stable and Efficient Lattice Methods for Linear Prediction,~ IEEE Trans. , Speech, and Signal Processing, vol. ASSP-25, pp. 423- 428, October 1977. 13. T. Alexander, "A Simple Noniterative Speech Excitation Algorithm Using LPC Residual," I EEE Trans. , Speech, and Signal Processing, vol. ASSP-33, pp. 432- 434, April 1985. 14. T. K. Hurd, Basic Electromagnetic Theor y, McGraw-Hill, New York, 1969.

The MSE contour in the v;"-plane corresponding to the MSE of 2e m;n on the error surface is an ellipse, centered at the origin, which intersects the v;" axes at vi = a and v; = b. Thus, it has been shown that the MSE contour e = 2cmin forms an ellipse in the v;"-plane. , is also straightforward and is explored in the problems at the end of the chapter. The result is that any constant MSE contour in the v;"-plane forms an ellipse centered at the origin, with major and minor axes aligned with the axes of the v;" coordinate space.

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