Algorithm Understanding of the J-Fast H<SUB>∞</SUB> Filter Based on Linear Prediction of Input Signal

Kiyoshi NISHIYAMA

doi:10.1587/transfun.E95.A.1175

Algorithm Understanding of the J-Fast H_∞ Filter Based on Linear Prediction of Input Signal

Kiyoshi NISHIYAMA

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The hyper H_∞ filter derived in our previous work provides excellent convergence, tracking, and robust performances for linear time-varying 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 J-fast H_∞ filter, is derived using a J-unitary array form, which is amenable to parallel processing. However, the J-fast 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 J-fast H_∞ filter. These findings are verified by computer simulations.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E95-A No.7 pp.1175-1179

Publication Date: 2012/07/01

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Online ISSN: 1745-1337

DOI: 10.1587/transfun.E95.A.1175

Type of Manuscript: LETTER

Category: Digital Signal Processing

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Kiyoshi NISHIYAMA, "Algorithm Understanding of the J-Fast H∞ Filter Based on Linear Prediction of Input Signal" in IEICE TRANSACTIONS on Fundamentals, vol. E95-A, no. 7, pp. 1175-1179, July 2012, doi: 10.1587/transfun.E95.A.1175.
Abstract: The hyper H_∞ filter derived in our previous work provides excellent convergence, tracking, and robust performances for linear time-varying 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 J-fast H_∞ filter, is derived using a J-unitary array form, which is amenable to parallel processing. However, the J-fast 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 J-fast H_∞ filter. These findings are verified by computer simulations.
URL: https://globals.ieice.org/en_transactions/fundamentals/10.1587/transfun.E95.A.1175/_p

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@ARTICLE{e95-a_7_1175,
author={Kiyoshi NISHIYAMA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Algorithm Understanding of the J-Fast H∞ Filter Based on Linear Prediction of Input Signal},
year={2012},
volume={E95-A},
number={7},
pages={1175-1179},
abstract={The hyper H_∞ filter derived in our previous work provides excellent convergence, tracking, and robust performances for linear time-varying 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 J-fast H_∞ filter, is derived using a J-unitary array form, which is amenable to parallel processing. However, the J-fast 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 J-fast H_∞ filter. These findings are verified by computer simulations.},
keywords={},
doi={10.1587/transfun.E95.A.1175},
ISSN={1745-1337},
month={July},}

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TY - JOUR
TI - Algorithm Understanding of the J-Fast H∞ Filter Based on Linear Prediction of Input Signal
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1175
EP - 1179
AU - Kiyoshi NISHIYAMA
PY - 2012
DO - 10.1587/transfun.E95.A.1175
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E95-A
IS - 7
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - July 2012
AB - The hyper H_∞ filter derived in our previous work provides excellent convergence, tracking, and robust performances for linear time-varying 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 J-fast H_∞ filter, is derived using a J-unitary array form, which is amenable to parallel processing. However, the J-fast 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 J-fast H_∞ filter. These findings are verified by computer simulations.
ER -