By Thomas S. Alexander
The construction of the textual content fairly begun in 1976 with the writer being concerned with a gaggle of researchers at Stanford college and the Naval Ocean platforms middle, San Diego. at the moment, adaptive ideas have been extra laboratory (and psychological) curiosities than the authorized and pervasive different types of sign processing that they have got turn into. Over the lasl 10 years, adaptive filters became common elements in telephony, information communications, and sign detection and monitoring structures. Their use and customer recognition will definitely purely elevate sooner or later. The mathematical rules underlying adaptive sign processing have been firstly attention-grabbing and have been my first event in seeing utilized arithmetic paintings for a paycheck. on account that that point, the appliance of much more complicated mathematical thoughts 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 specialist journals, that's often really focused, concise, and complex, and the graduate school room and study surroundings the place underlying ideas are frequently extra important.
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Additional resources for Adaptive Signal Processing: Theory and Applications
H. Gray, "On Autocorrel ation Equations as Applied to Speech Analysis," IEEE Trans. Audio and Electroacoustics, vol. AV-21, pp. 69-79, February 1973. 11. R. W. Schafer, Digital Processing of Speech Signals, Prentice-Hall. Englewood Cliffs, NJ, 1978. 12. s. Jayant and P. Noll, Digital Coding of Waveforms, Prentice-Hall, Englewood Cliffs, NJ, 1984. 13. A. Papoulis, Probability, Rondom Variables , and Stochastic Processes, McGrawHill, New York, 1984. 14. V. W. Schafer, Digital Signol Processing, Prentice-Hall, Englewood Cliffs, NJ, 1975.
3. 7) i-I These operations produce [ ] ,-, I (p-I ) - j Gp(Z) -_ GpI _l(z) - kp Z- p - ~ Wp _j Z . 8) may be simplified by considering the bracketed term on the right-hand side. This term introduces the concept of the backward prediction error (BPE) fiiter , which will be very useful in the remainder of the text. The important point, however, is to realize that the concept of BPE results entirely from using Durbin's algorithm, and is simply the term chosen to describe the operations. 8). •• - W(P - l ),-(P-I) (339) p-I·· .
The lattice filte r structure follows directly from examining the time series of the FPE and BPE filter outputs. 4) was derived specifically for the Nth order filter, but is a completely general result as holds for any order 1 :::;; P :os; N. 1 (a) Single stage of the linear prediction lattice filter. (b) Cascade of stages of form Nth order linear prediction filler. where X(z)is the z-transform of the signal x(n). 3. 20) Z- I X(Z)G! _I (z) - k,X(z)Gt_1(z). 21) £:(z) = Z-I £:_I(Z) - k,£' _I(z). 22) by taking the inverse z-tranforms: et(n) = et_l(n) - k,e!
Adaptive Signal Processing: Theory and Applications by Thomas S. Alexander