WAVELET VARIANCE, ALLAN VARIANCE, AND LEAKAGE

Wavelets have recently been a subject of great interest in geophysics, mathematics and signal processing. The discrete wavelet transform can be used to decompose a time series with respect to a set of basis fun ctions, each one of which is associated with a particular scale. The p roperties of a time series at different scales can then be summarized by the wavelet variance, which decomposes the variance of a time serie s on a scale by scale basis. The wavelet variance corresponding to som e of the recently discovered wavelets can provide a more accurate conv ersion between the time and frequency domains than can be accomplished using the Allan variance. This increase in accuracy is due to the fac t that these wavelet variances give better protection against leakage than does the Allan variance.