Khalidov, Ildarde Ville, Dimitri VanBlu, ThierryUnser, Michael2012-07-042012-07-042012-07-04200710.1117/12.734606https://infoscience.epfl.ch/handle/20.500.14299/83485WOS:000252227400023Probably, the most important property of wavelets for signal processing is their multiscale derivative-like behavior when applied to functions. In order to extend the class of problems that can profit of wavelet-based techniques, we propose to build new families of wavelets that behave like an arbitrary scale-covariant operator. Our extension is general and includes many known wavelet bases. At the same time, the method takes advantage a fast filterbank decomposition-reconstruction algorithm. We give necessary conditions for the scale-covariant operator to admit our wavelet construction, and we provide examples of new wavelets that can be obtained with our method.waveletssplinesdifferential operatorsGreen's functionscontinuous-time signal processingmultiresolution approximationmultiresolution analysisSplinestext::conference output::conference proceedings::conference paper