Removal of the Phase Oscillation Observed in Wavelet Analysis in Terms of Spatial Filtering
Makoto Iima, Sadayoshi Toh · Journal of the Physical Society of Japan · 1998
In the analysis of orthonormal wavelet, standard definitions of physical quantities such as energy in wavelet space are not free from spatial oscillation intrinsic to wavelet base function, i.e., phase in contrast to the Fourier analysis. Moreover the energy summed over a scale is not translationally invariant. To remove the phase, we propose a kind of spatial averaging in terms of extended continuous wavelet. The translational invariance of energy is recovered by means of this averaging method. This method is also applied to the transfer functions which were defined in terms of orthonormal wavelet in the previous paper [Phys. Rev. E 52 (1995) 6189].