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Algorithm Understanding of the JFast H_{∞} Filter Based on Linear Prediction of Input Signal
Kiyoshi NISHIYAMA
Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Vol.E95A
No.7
pp.11751179 Publication Date: 2012/07/01
Online ISSN: 17451337
DOI: 10.1587/transfun.E95.A.1175
Print ISSN: 09168508 Type of Manuscript: LETTER Category: Digital Signal Processing Keyword: H_{∞} filter, fast algorithm, forward linear prediction, backward linear prediction, system identification,
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Summary:
The hyper H_{∞} filter derived in our previous work provides excellent convergence, tracking, and robust performances for linear timevarying system identification. Additionally, a fast algorithm of the hyper H_{∞} filter, called the fast H_{∞} filter, is successfully developed so that identification of linear system with impulse response of length N is performed at a computational complexity of O(N). The gain matrix of the fast filter is recursively calculated through estimating the forward and backward linear prediction coefficients of an input signal. This suggests that the fast H_{∞} filter may be applicable to linear prediction of the signal. On the other hand, an alternative fast version of the hyper H_{∞} filter, called the Jfast H_{∞} filter, is derived using a Junitary array form, which is amenable to parallel processing. However, the Jfast H_{∞} filter explicitly includes no linear prediction of input signals in the algorithm. This work reveals that the forward and backward linear prediction coefficients and error powers of the input signal are indeed included in the recursive variables of the Jfast H_{∞} filter. These findings are verified by computer simulations.

