J. Qiu et al., THE LEAKAGE PROBLEM OF ORTHONORMAL WAVELET TRANSFORMS WHEN APPLIED TOATMOSPHERIC-TURBULENCE, JOURNAL OF GEOPHYSICAL RESEARCH-ATMOSPHERES, 100(D12), 1995, pp. 25769-25779
Orthonormal wavelet transforms are becoming common in the study of tur
bulence phenomena. Although they are powerful tools in representing a
signal, their use as tools to study the characteristics of turbulent s
tructures can create appreciable errors in interpretation. It is shown
here that although the orthonormal wavelet transform is computational
ly economical by taking advantage of multiresolution analysis, it has
insufficient resolution in both scale and location to resolve detailed
information of turbulence structures. Lacking in resolution, the ener
gy at a particular frequency (or wavelength) may leak into neighboring
frequencies and may pass down to smaller scales to produce an artific
ial ''cascade'' of energy (with a slope close to -2/3). The choice of
wavelet basis function is important to the wavelet spectrum, especiall
y in the study of turbulence flows dominated by coherent structures, s
ince the method most accurately senses energy contained in pulses that
have a similar pattern to the wavelet function. To use the method as
a filter can be problematic owing to the low resolution of the orthono
rmal wavelet transform; nonorthonormal wavelet analysis should be empl
oyed when high resolution is important. When orthonormal wavelet trans
forms have to be used for signal analysis, segmented averaging should
be employed.