Information Theory

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

By Thomas S. Alexander

The construction of the textual content particularly all started in 1976 with the writer being concerned with a bunch of researchers at Stanford college and the Naval Ocean structures heart, San Diego. at the moment, adaptive suggestions have been extra laboratory (and psychological) curiosities than the permitted and pervasive different types of sign processing that they've develop into. Over the lasl 10 years, adaptive filters became normal elements in telephony, info communications, and sign detection and monitoring platforms. Their use and purchaser popularity will unquestionably merely raise sooner or later. The mathematical rules underlying adaptive sign processing have been before everything interesting and have been my first event in seeing utilized arithmetic paintings for a paycheck. when you consider that that point, the appliance of much more complex mathematical strategies have saved the realm of adaptive sign processing as fascinating as these preliminary days. The textual content seeks to be a bridge among the open literature within the specialist journals, that's frequently rather focused, concise, and complicated, and the graduate lecture room and examine surroundings the place underlying ideas are usually extra important.

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12), which will be very beneficial in analytical work. ln and £ = 3£mio' (b) Projection of 4"'ln and 38"'ln contours in v;'-plane. weights and additional linear weight terms. 8) do not alter the shape of the MSE surface. Only its orientation relative to some set of coordinate axes is changed. These transformations are very useful and quite powerful and will be used again in Chapters 4 and 5 to simplify the interpretation of adaptive filler properties. One additional property of the MSE surface is that the entire family of MSE contours are only scaled versions of that for e = em;n' To see this.

561 - 580, April 1975. 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.

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. The contours intersect the v;" axes at values dependent upon the eigenvalues of RNN and the specific MSE value chosen. These results allow a simple method for visualizing the MSE surface via its error contours.

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