Multi-Band Decomposition of the Linear Prediction Error Applied to Adaptive AR Spectral Estimation

Fernando Gil V. RESENDE Jr.; Keiichi TOKUDA; Mineo KANEKO; Akinori NISHIHARA

Multi-Band Decomposition of the Linear Prediction Error Applied to Adaptive AR Spectral Estimation

Fernando Gil V. RESENDE Jr., Keiichi TOKUDA, Mineo KANEKO, Akinori NISHIHARA

Full Text Views

0

Share
Cite this

Summary :

A new structure for adaptive AR spectral estimation based on multi-band decomposition of the linear prediction error is introduced and the mathematical background for the soulution of the related adaptive filtering problem is derived. The presented structure gives rise to AR spectral estimates that represent the true underlying spectrum with better fidelity than conventional LS methods by allowing an arbitrary trade-off between variance of spectral estimates and tracking ability of the estimator along the frequency spectrum. The linear prediction error is decomposed through a filter bank and components of each band are analyzed by different window lengths, allowing long windows to track slowly varying signals and short windows to observe fastly varying components. The correlation matrix of the input signal is shown to satisfy both time-update and order-update properties for rectangular windowing functions, and an RLS algorithm based on each property is presented. Adaptive forward and backward relations are used to derive a mathematical framework that serves as a basis for the design of fast RLS alogorithms. Also, computer experiments comparing the performance of conventional and the proposed multi-band methods are depicted and discussed.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E80-A No.2 pp.365-376

Publication Date: 1997/02/25

Publicized

Online ISSN

DOI

Type of Manuscript

Category: Digital Signal Processing

Cite this

Copy

Fernando Gil V. RESENDE Jr., Keiichi TOKUDA, Mineo KANEKO, Akinori NISHIHARA, "Multi-Band Decomposition of the Linear Prediction Error Applied to Adaptive AR Spectral Estimation" in IEICE TRANSACTIONS on Fundamentals, vol. E80-A, no. 2, pp. 365-376, February 1997, doi: .
Abstract: A new structure for adaptive AR spectral estimation based on multi-band decomposition of the linear prediction error is introduced and the mathematical background for the soulution of the related adaptive filtering problem is derived. The presented structure gives rise to AR spectral estimates that represent the true underlying spectrum with better fidelity than conventional LS methods by allowing an arbitrary trade-off between variance of spectral estimates and tracking ability of the estimator along the frequency spectrum. The linear prediction error is decomposed through a filter bank and components of each band are analyzed by different window lengths, allowing long windows to track slowly varying signals and short windows to observe fastly varying components. The correlation matrix of the input signal is shown to satisfy both time-update and order-update properties for rectangular windowing functions, and an RLS algorithm based on each property is presented. Adaptive forward and backward relations are used to derive a mathematical framework that serves as a basis for the design of fast RLS alogorithms. Also, computer experiments comparing the performance of conventional and the proposed multi-band methods are depicted and discussed.
URL: https://globals.ieice.org/en_transactions/fundamentals/10.1587/e80-a_2_365/_p

Copy

@ARTICLE{e80-a_2_365,
author={Fernando Gil V. RESENDE Jr., Keiichi TOKUDA, Mineo KANEKO, Akinori NISHIHARA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Multi-Band Decomposition of the Linear Prediction Error Applied to Adaptive AR Spectral Estimation},
year={1997},
volume={E80-A},
number={2},
pages={365-376},
abstract={A new structure for adaptive AR spectral estimation based on multi-band decomposition of the linear prediction error is introduced and the mathematical background for the soulution of the related adaptive filtering problem is derived. The presented structure gives rise to AR spectral estimates that represent the true underlying spectrum with better fidelity than conventional LS methods by allowing an arbitrary trade-off between variance of spectral estimates and tracking ability of the estimator along the frequency spectrum. The linear prediction error is decomposed through a filter bank and components of each band are analyzed by different window lengths, allowing long windows to track slowly varying signals and short windows to observe fastly varying components. The correlation matrix of the input signal is shown to satisfy both time-update and order-update properties for rectangular windowing functions, and an RLS algorithm based on each property is presented. Adaptive forward and backward relations are used to derive a mathematical framework that serves as a basis for the design of fast RLS alogorithms. Also, computer experiments comparing the performance of conventional and the proposed multi-band methods are depicted and discussed.},
keywords={},
doi={},
ISSN={},
month={February},}

Copy

TY - JOUR
TI - Multi-Band Decomposition of the Linear Prediction Error Applied to Adaptive AR Spectral Estimation
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 365
EP - 376
AU - Fernando Gil V. RESENDE Jr.
AU - Keiichi TOKUDA
AU - Mineo KANEKO
AU - Akinori NISHIHARA
PY - 1997
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E80-A
IS - 2
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - February 1997
AB - A new structure for adaptive AR spectral estimation based on multi-band decomposition of the linear prediction error is introduced and the mathematical background for the soulution of the related adaptive filtering problem is derived. The presented structure gives rise to AR spectral estimates that represent the true underlying spectrum with better fidelity than conventional LS methods by allowing an arbitrary trade-off between variance of spectral estimates and tracking ability of the estimator along the frequency spectrum. The linear prediction error is decomposed through a filter bank and components of each band are analyzed by different window lengths, allowing long windows to track slowly varying signals and short windows to observe fastly varying components. The correlation matrix of the input signal is shown to satisfy both time-update and order-update properties for rectangular windowing functions, and an RLS algorithm based on each property is presented. Adaptive forward and backward relations are used to derive a mathematical framework that serves as a basis for the design of fast RLS alogorithms. Also, computer experiments comparing the performance of conventional and the proposed multi-band methods are depicted and discussed.
ER -