Sparse Representation with Harmonic Wavelets

A simple method, based on harmonic wavelets, is proposed for the decomposition of a suitable signal into a periodic function and a pulse. It will be shown that, under some general conditions, by a simple projection into two disjoint orthogonal space of functions the periodic component of the signal can be separated from the localized part. The proposed algorithm, gives an approximate (scale depending) decomposition and can be used also for an efficient denoising (as shown in the final examples).