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

Shigeo WADA  Nao ITO  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E87-A   No.2   pp.417-423
Publication Date: 2004/02/01
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Digital Signal Processing
1/f process,  parameter estimation,  wavelet,  EM algorithm,  

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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.