Improvement of Wavelet Based Parameter Estimations of Nearly 1/<I>f</I> Processes

Shigeo WADA; Nao ITO

Improvement of Wavelet Based Parameter Estimations of Nearly 1/f Processes

Shigeo WADA, Nao ITO

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Nearly 1/f processes are known as important stochastic models for scale invariant data analysis in a number of fields. In this paper, two parameter estimation methods of nearly 1/f processes based on wavelets are proposed. The conventional method based on wavelet transform with EM algorithm does not give the reliable parameter estimation value when the data length is short. Moreover, the precise parameter value is not estimated when the spectrum gap exists in 1/f processes. First, in order to improve the accuracy of the estimation when the data length is short, a parameter estimation method based on wavelet transform with complementary sampling is proposed. Next, in order to reduce the effect of spectrum gap, a parameter estimation method based on wavelet packet with EM algorithm is proposed. Simulation results are given to verify the effectiveness of the proposed methods.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E87-A No.2 pp.417-423

Publication Date: 2004/02/01

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Type of Manuscript: PAPER

Category: Digital Signal Processing

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Shigeo WADA, Nao ITO, "Improvement of Wavelet Based Parameter Estimations of Nearly 1/f Processes" in IEICE TRANSACTIONS on Fundamentals, vol. E87-A, no. 2, pp. 417-423, February 2004, doi: .
Abstract: Nearly 1/f processes are known as important stochastic models for scale invariant data analysis in a number of fields. In this paper, two parameter estimation methods of nearly 1/f processes based on wavelets are proposed. The conventional method based on wavelet transform with EM algorithm does not give the reliable parameter estimation value when the data length is short. Moreover, the precise parameter value is not estimated when the spectrum gap exists in 1/f processes. First, in order to improve the accuracy of the estimation when the data length is short, a parameter estimation method based on wavelet transform with complementary sampling is proposed. Next, in order to reduce the effect of spectrum gap, a parameter estimation method based on wavelet packet with EM algorithm is proposed. Simulation results are given to verify the effectiveness of the proposed methods.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e87-a_2_417/_p

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@ARTICLE{e87-a_2_417,
author={Shigeo WADA, Nao ITO, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Improvement of Wavelet Based Parameter Estimations of Nearly 1/f Processes},
year={2004},
volume={E87-A},
number={2},
pages={417-423},
abstract={Nearly 1/f processes are known as important stochastic models for scale invariant data analysis in a number of fields. In this paper, two parameter estimation methods of nearly 1/f processes based on wavelets are proposed. The conventional method based on wavelet transform with EM algorithm does not give the reliable parameter estimation value when the data length is short. Moreover, the precise parameter value is not estimated when the spectrum gap exists in 1/f processes. First, in order to improve the accuracy of the estimation when the data length is short, a parameter estimation method based on wavelet transform with complementary sampling is proposed. Next, in order to reduce the effect of spectrum gap, a parameter estimation method based on wavelet packet with EM algorithm is proposed. Simulation results are given to verify the effectiveness of the proposed methods.},
keywords={},
doi={},
ISSN={},
month={February},}

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TY - JOUR
TI - Improvement of Wavelet Based Parameter Estimations of Nearly 1/f Processes
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 417
EP - 423
AU - Shigeo WADA
AU - Nao ITO
PY - 2004
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E87-A
IS - 2
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - February 2004
AB - Nearly 1/f processes are known as important stochastic models for scale invariant data analysis in a number of fields. In this paper, two parameter estimation methods of nearly 1/f processes based on wavelets are proposed. The conventional method based on wavelet transform with EM algorithm does not give the reliable parameter estimation value when the data length is short. Moreover, the precise parameter value is not estimated when the spectrum gap exists in 1/f processes. First, in order to improve the accuracy of the estimation when the data length is short, a parameter estimation method based on wavelet transform with complementary sampling is proposed. Next, in order to reduce the effect of spectrum gap, a parameter estimation method based on wavelet packet with EM algorithm is proposed. Simulation results are given to verify the effectiveness of the proposed methods.
ER -