Consistency of Frequency Estimates Based on the Wavelet Transform
Ritei Shibata, Mutsumi Takagiwa · Journal of Time Series Analysis · 1997
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