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Consistency of Frequency Estimates Based on the Wavelet Transform
Author(s) -
Shibata Ritei,
Takagiwa Mutsumi
Publication year - 1997
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/1467-9892.00072
Subject(s) - wavelet , mathematics , wavelet transform , discrete wavelet transform , consistency (knowledge bases) , stationary wavelet transform , harmonic wavelet transform , second generation wavelet transform , wavelet packet decomposition , dilation (metric space) , continuous wavelet transform , lifting scheme , algorithm , artificial intelligence , discrete mathematics , computer science , combinatorics
The consistency of the least squares estimate of frequencies modulated in amplitude is investiga ted. It is proved that the estimate based on the wavelet transform is consistent when dilation and translation parameters of the wavelet transform as well as the sampling points are carefully chosen in order to preserve consistency. Our theorem shows that an intuitive method proposed by P. Guillemain et al . (Estimation of spectral lines with the help of the wavelet transform: application in NMR spectroscopy. In Wavelets and Applications (ed. Y. Meyer). New York: Springer, 1992, pp. 38–68) works well for the non‐noisy case but does not work well for the noisy case. A key to the consistency is the use of the localization property of the wavelet transform