Scrub data with scale-invariant nonlinear digital filters

Simple linear digital filters are useful in many applications. Linearity is a significant practical advantage that you can exploit to develop useful classifications (such as lowpass, highpass, or bandpass filters), rules of thumb (such as "Highpass filters require both positive and negative filter coefficients"), and design procedures (see, for example, Reference 1). Unfortunately, some applications require nonlinear filters. Such filters are capable of implementing a vastly wider range of qualitative behavior, but they are harder to design and analyze than linear filters. One reason for this difficulty is that the range of possible nonlinear-filter types is enormous and extremely heterogeneous: Two classes of nonlinear filters may be as dissimilar to each other as they are to the class of linear filters. In fact, as others have repeatedly observed, the difficulty is partly inherent in the term "nonlinear," which characterizes an enormous class of systems by their lack of a unique property. The situation is analogous to considering "nonkangaroo zoology." The class of nonkangaroos includes both all species of octopus and all species of beetle, two subsets that seem as dissimilar to each other as they are to kangaroos.