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Time localization techniques for wavelet transforms

We consider the following pair of problems related to orthonormal compactly supported wavelet expansions: (1) Given a wavelet coefficient with its nominal scale and position indices, find the precise location of the transient signal feature which produced it; (2) Given two collections of wavelet coefficients, determine whether they arise from a periodic signal and its translate, and if so find the translation which maps one into the other. Both problems may be solved by traditional means after inverting the wavelet transform, but we propose two alternative algorithms which rely solely on the wavelet coefficients themselves.