Convergence Vectors in System Identification with an NLMS Algorithm for Sinusoidal Inputs

Yuki SATOMI; Arata KAWAMURA; Youji IIGUNI

doi:10.1587/transfun.E95.A.1692

Convergence Vectors in System Identification with an NLMS Algorithm for Sinusoidal Inputs

Yuki SATOMI, Arata KAWAMURA, Youji IIGUNI

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For an adaptive system identification filter with a stochastic input signal, a coefficient vector updated with an NLMS algorithm converges in the sense of ensemble average and the expected convergence vector has been revealed. When the input signal is periodic, the convergence of the adaptive filter coefficients has also been proved. However, its convergence vector has not been revealed. In this paper, we derive the convergence vector of adaptive filter coefficients updated with the NLMS algorithm in system identification for deterministic sinusoidal inputs. Firstly, we derive the convergence vector when a disturbance does not exist. We show that the derived convergence vector depends only on the initial vector and the sinusoidal frequencies, and it is independent of the step-size for adaptation, sinusoidal amplitudes, and phases. Next, we derive the expected convergence vector when the disturbance exists. Simulation results support the validity of the derived convergence vectors.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E95-A No.10 pp.1692-1699

Publication Date: 2012/10/01

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Online ISSN: 1745-1337

DOI: 10.1587/transfun.E95.A.1692

Type of Manuscript: PAPER

Category: Digital Signal Processing

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Yuki SATOMI, Arata KAWAMURA, Youji IIGUNI, "Convergence Vectors in System Identification with an NLMS Algorithm for Sinusoidal Inputs" in IEICE TRANSACTIONS on Fundamentals, vol. E95-A, no. 10, pp. 1692-1699, October 2012, doi: 10.1587/transfun.E95.A.1692.
Abstract: For an adaptive system identification filter with a stochastic input signal, a coefficient vector updated with an NLMS algorithm converges in the sense of ensemble average and the expected convergence vector has been revealed. When the input signal is periodic, the convergence of the adaptive filter coefficients has also been proved. However, its convergence vector has not been revealed. In this paper, we derive the convergence vector of adaptive filter coefficients updated with the NLMS algorithm in system identification for deterministic sinusoidal inputs. Firstly, we derive the convergence vector when a disturbance does not exist. We show that the derived convergence vector depends only on the initial vector and the sinusoidal frequencies, and it is independent of the step-size for adaptation, sinusoidal amplitudes, and phases. Next, we derive the expected convergence vector when the disturbance exists. Simulation results support the validity of the derived convergence vectors.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E95.A.1692/_p

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@ARTICLE{e95-a_10_1692,
author={Yuki SATOMI, Arata KAWAMURA, Youji IIGUNI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Convergence Vectors in System Identification with an NLMS Algorithm for Sinusoidal Inputs},
year={2012},
volume={E95-A},
number={10},
pages={1692-1699},
abstract={For an adaptive system identification filter with a stochastic input signal, a coefficient vector updated with an NLMS algorithm converges in the sense of ensemble average and the expected convergence vector has been revealed. When the input signal is periodic, the convergence of the adaptive filter coefficients has also been proved. However, its convergence vector has not been revealed. In this paper, we derive the convergence vector of adaptive filter coefficients updated with the NLMS algorithm in system identification for deterministic sinusoidal inputs. Firstly, we derive the convergence vector when a disturbance does not exist. We show that the derived convergence vector depends only on the initial vector and the sinusoidal frequencies, and it is independent of the step-size for adaptation, sinusoidal amplitudes, and phases. Next, we derive the expected convergence vector when the disturbance exists. Simulation results support the validity of the derived convergence vectors.},
keywords={},
doi={10.1587/transfun.E95.A.1692},
ISSN={1745-1337},
month={October},}

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TY - JOUR
TI - Convergence Vectors in System Identification with an NLMS Algorithm for Sinusoidal Inputs
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1692
EP - 1699
AU - Yuki SATOMI
AU - Arata KAWAMURA
AU - Youji IIGUNI
PY - 2012
DO - 10.1587/transfun.E95.A.1692
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E95-A
IS - 10
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - October 2012
AB - For an adaptive system identification filter with a stochastic input signal, a coefficient vector updated with an NLMS algorithm converges in the sense of ensemble average and the expected convergence vector has been revealed. When the input signal is periodic, the convergence of the adaptive filter coefficients has also been proved. However, its convergence vector has not been revealed. In this paper, we derive the convergence vector of adaptive filter coefficients updated with the NLMS algorithm in system identification for deterministic sinusoidal inputs. Firstly, we derive the convergence vector when a disturbance does not exist. We show that the derived convergence vector depends only on the initial vector and the sinusoidal frequencies, and it is independent of the step-size for adaptation, sinusoidal amplitudes, and phases. Next, we derive the expected convergence vector when the disturbance exists. Simulation results support the validity of the derived convergence vectors.
ER -