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The individually normalized least mean square (INLMS) algorithm is proposed as an adaptive algorithm suitable for the fixed point processing. The convergence property of the INLMS algorithm, however, is not yet analyzed enough. This paper first derives an equation describing the convergence property by exploiting the technique of expressing the INLMS algorithm as a first order infinite impulse response (IIR) filter. According to the equation derived thus, the decreasing process of the estimation error is represented as the response of another IIR filter expression. By using the representation, this paper second derives the convergence condition of the INLMS algorithm as the range of the step size making a low path filter of the latter IIR filter. This paper also derives the step size maximizing the convergence speed as the maximum coefficient of the latter IIR filter and finally clarifies the range of the step size recommended in the practical system design.

- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E83-A No.8 pp.1539-1544

- Publication Date
- 2000/08/25

- Publicized

- Online ISSN

- DOI

- Type of Manuscript
- Special Section PAPER (Special Section on Digital Signal Processing)

- Category
- Adaptive Signal Processing

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Kensaku FUJII, Juro OHGA, "Analysis on Convergence Property of INLMS Algorithm Suitable for Fixed Point Processing" in IEICE TRANSACTIONS on Fundamentals,
vol. E83-A, no. 8, pp. 1539-1544, August 2000, doi: .

Abstract: The individually normalized least mean square (INLMS) algorithm is proposed as an adaptive algorithm suitable for the fixed point processing. The convergence property of the INLMS algorithm, however, is not yet analyzed enough. This paper first derives an equation describing the convergence property by exploiting the technique of expressing the INLMS algorithm as a first order infinite impulse response (IIR) filter. According to the equation derived thus, the decreasing process of the estimation error is represented as the response of another IIR filter expression. By using the representation, this paper second derives the convergence condition of the INLMS algorithm as the range of the step size making a low path filter of the latter IIR filter. This paper also derives the step size maximizing the convergence speed as the maximum coefficient of the latter IIR filter and finally clarifies the range of the step size recommended in the practical system design.

URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e83-a_8_1539/_p

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@ARTICLE{e83-a_8_1539,

author={Kensaku FUJII, Juro OHGA, },

journal={IEICE TRANSACTIONS on Fundamentals},

title={Analysis on Convergence Property of INLMS Algorithm Suitable for Fixed Point Processing},

year={2000},

volume={E83-A},

number={8},

pages={1539-1544},

abstract={The individually normalized least mean square (INLMS) algorithm is proposed as an adaptive algorithm suitable for the fixed point processing. The convergence property of the INLMS algorithm, however, is not yet analyzed enough. This paper first derives an equation describing the convergence property by exploiting the technique of expressing the INLMS algorithm as a first order infinite impulse response (IIR) filter. According to the equation derived thus, the decreasing process of the estimation error is represented as the response of another IIR filter expression. By using the representation, this paper second derives the convergence condition of the INLMS algorithm as the range of the step size making a low path filter of the latter IIR filter. This paper also derives the step size maximizing the convergence speed as the maximum coefficient of the latter IIR filter and finally clarifies the range of the step size recommended in the practical system design.},

keywords={},

doi={},

ISSN={},

month={August},}

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TY - JOUR

TI - Analysis on Convergence Property of INLMS Algorithm Suitable for Fixed Point Processing

T2 - IEICE TRANSACTIONS on Fundamentals

SP - 1539

EP - 1544

AU - Kensaku FUJII

AU - Juro OHGA

PY - 2000

DO -

JO - IEICE TRANSACTIONS on Fundamentals

SN -

VL - E83-A

IS - 8

JA - IEICE TRANSACTIONS on Fundamentals

Y1 - August 2000

AB - The individually normalized least mean square (INLMS) algorithm is proposed as an adaptive algorithm suitable for the fixed point processing. The convergence property of the INLMS algorithm, however, is not yet analyzed enough. This paper first derives an equation describing the convergence property by exploiting the technique of expressing the INLMS algorithm as a first order infinite impulse response (IIR) filter. According to the equation derived thus, the decreasing process of the estimation error is represented as the response of another IIR filter expression. By using the representation, this paper second derives the convergence condition of the INLMS algorithm as the range of the step size making a low path filter of the latter IIR filter. This paper also derives the step size maximizing the convergence speed as the maximum coefficient of the latter IIR filter and finally clarifies the range of the step size recommended in the practical system design.

ER -