By Maurice Bellanger
This article emphasizes the problematic dating among adaptive filtering and sign research - highlighting stochastic strategies, sign representations and homes, analytical instruments, and implementation equipment. This moment variation contains new chapters on adaptive concepts in communications and rotation-based algorithms. It presents functional functions in details, estimation, and circuit theories.
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Extra info for Adaptive Digital Filters (Signal Processing and Communications)
Is the line spectrum of the deterministic component, the two components being uncorrelated. 11. HARMONIC DECOMPOSITION The fundamental decomposition is used in signal analysis as a reference for selecting a strategy . As an illustration let us consider the case, frequently occurring in practice, where the signal to be analyzed is given as a set of 2 N þ 1 autocorrelation coefﬁcients rðpÞ with ÀN 4 p 4 N, available from a measuring procedure. To perform the analysis, we have two extreme hypotheses.
14 Image signal: three lines of a black-and-white picture. ples, namely speech, radar, and image samples, have been selected to illustrate the theory. EXERCISES 1. Calculate the z-transform YR ðzÞ of the damped cosinusoid ( 0; n<0 yR ðnÞ ¼ eÀ0:1n cos n ; n 5 0 2 and show the poles in the complex plane. Give the signal energy spectrum and verify the energy relationship Z 1 X 1 2 yR ðnÞ ¼ Y ðzÞYR ðzÀ1 ÞzÀ1 dz Ey ¼ 2j jzj¼1 R n¼0 2. Give the coefﬁcients, initial conditions, and diagram of the secondorder section which generates yR ðnÞ.
2:105Þ Ea ¼ 2 À or, in terms of z-transforms, Z 1 dz AðzÞAðzÀ1 ÞSðzÞ Ea ¼ j2 jzj¼1 z TM Copyright n 2001 by Marcel Dekker, Inc. All Rights Reserved. ð2:106Þ FIG. 8 Linear prediction ﬁlter and inverse ﬁlter. where AðzÞ is the transfer function of the prediction error ﬁlter. The prediction ﬁlter coefﬁcients depend only on the input signal, and the error power can be expressed as a function of Sðe j! Þ only. To derive that expression, we must ﬁrst show that the prediction error ﬁlter is minimum phase; in other words, all its zeros are inside or on the unit circle in the complex z-plane.
Adaptive Digital Filters (Signal Processing and Communications) by Maurice Bellanger