ANALYTIC WAVELETS AND MULTIRESOLUTION ANALYSIS A NOTE ON CERTAIN ORTHOGONALITY CONDITIONS

The main disadvantages of the Fourier series and transforms are left behind by a new tool: wavelets! The properties of wavelets are well presented, apart from continuity, by the oldest example ‐ the Haar wavelets. This work deals with expanding wavelets on the complex plane using their analytic representations. Here are reviewed analytic wavelets and their basic properties. The corresponding multiresolution analysis, however, does not preserve the ortogonality it had on the real line. Here is given a consequence regarding the ortogonality of the basis generated by the scaling function. Under some conditions, the orthogonality is preserved, as seen with the Shannon wavelets.