By Maurice Bellanger
This article emphasizes the problematic dating among adaptive filtering and sign research - highlighting stochastic tactics, sign representations and houses, analytical instruments, and implementation equipment. This moment version comprises new chapters on adaptive concepts in communications and rotation-based algorithms. It offers useful functions in details, estimation, and circuit theories.
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Additional info for Adaptive Digital Filters (Signal Processing and Communications)
Linear prediction is useful for classifying signals and, particular, distinguishing between deterministic and random processes. 9. PREDICTABLE SIGNALS A signal xðnÞ is predictable if and only if its prediction error power is null: Z 1 Ea ¼ jAðe j! Þj2 Sðe j! Þ d! ¼ 0 ð2:121Þ 2 À or, in the time domain, TM Copyright n 2001 by Marcel Dekker, Inc. All Rights Reserved. xðnÞ ¼ 1 X ai xðn À iÞ ð2:122Þ i¼1 which means that the present value xðnÞ of the signal can be expressed in terms of its past values.
13 FMCW radar signal. as main parameters, the ACF, the spectrum, and the generating model. Periodic signals have been analyzed ﬁrst. Then random signals have been deﬁned, with attention being focused on wide-sense stationary signals; they have second-order statistics which are independent of time. Synthetic random signals can be generated by a ﬁlter fed with white noise. The Gaussian amplitude distribution is especially important because of its nice statistical properties, but also because it is a model adequate for many real situations.
Where ð2:86Þ ÀaN 0 ÁÁÁ For real signals, the ﬁrst ðN þ 1Þ ACF terms are obtained from the equation 3 2 3 2 rð0Þ dð0Þ 6 rð1Þ 7 6 dð1Þ 7 7 6 7 2 0 À1 6 ð2:87Þ 6 .. 7 ¼ e ½A þ A 6 .. 7 4 . 5 4 . 5 rðNÞ dðNÞ In summary, the procedure to calculate the ACF of an ARMA signal from the generating ﬁlter coefﬁcients is as follows: TM Copyright n 2001 by Marcel Dekker, Inc. All Rights Reserved. 1. 2. 3. 4. 82). Compute the auxiliary variables dðpÞ for 0 4 p 4 N. 87). 68) to derive rðpÞ when p 5 N þ 1.
Adaptive Digital Filters (Signal Processing and Communications) by Maurice Bellanger