A class of robust nonlinear filters for signal decomposition and filtering, utilizing the Haar basis

A class of robust nonlinear filters for signal decomposition and filtering based on the Haar basis is discussed. The nonlinear filters with window width 2N+1 are shown to be linear over the PICO(N+1) signals (piecewise constant signals) where the minimum width of a constant region is N+1. Next, passband filtering of PICO signals, edge enhancement, and an optimality criterion for filtering of PICO signals is discussed. An application of the filters to biological data (non-PICO) is then demonstrated