Abstract
We define and prove the existence of crossings of wavelet coefficients translated by integer multiples of the numerator of a continued fraction convergent of the ratio of the sampling interval to the period of the wavelet coefficients. Crossings are found to be translation invariant ±1. Intervals between crossings are analyzed for wavelets with n vanishing moments. These wavelets act as multiscale differential operators. These crossings reveal different locations in the period where there is equality in the nth derivative of an averaging of the signal. These results will be employed in the estimation of frequency components in future publications.
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