Properties of a Series of Nested Median Filters, Namely the Data Sieve

The data sieve is a series of nested median filters of increasing window width. Likewise, the root data sieve is a series of root median filters such that S' sub(m) = r sub(m) (S' sub(m-1)); where S' sub(0) = r sub(0) (D) = D, D is the original data signal sampled at regular intervals (n samples) and r sub(m) is a root median filter of window = 2m + 1 samples. These filters remove impulsive signals embedded in oscillatory regions better than root median filters. It is also shown that unlike a median filter, the mth root median filter in the series only removes pulses represented by m samples, and oscillations are, under these conditions, nothing more than a contiguous series of rectangular pulses separated by m samples. Furthermore, a root data sieve comprising a series of n stages can be used as a set of bandpass filters to reexpress D as a root set of rectangular pulses. These can be used to generate a 'rectangular-pulse spectrum.' By exploiting both the large extent of run length coding possible in the course of applying s sub(m) and the systematic way the algorithm divides up the problem, an experimental order complexity of approximately n super(1.8) can readily be achieved, and further improvements can be expected.