NDLI: Sorting continuous-time signals: analog median and median-type filters

Content Provider	IEEE Xplore Digital Library
Author	Ferreira, P.J.S.G.
Copyright Year	1991
Abstract	There are two natural orderings in signals: temporal order and rank order. There is no compelling reason to explore only one of these orderings, either in the discrete-time or in the continuous-time case. Nevertheless, the concept of rank order for continuous-time signals remains virtually neglected, which is in striking contrast to the discrete-time case: ranked order discrete-time filters, of which the running median is the most common example, have been intensively studied for three decades. The dependence of these nonlinear systems on the order statistics of the input samples stands in contrast with the tapped delay line filter, which depends on temporal order only. However, continuous-time signals can also be meaningfully sorted: a fact that is explored in this paper to define and study the analog median filter and other ranked-order filters. The paper introduces the basic tools needed to analyze and understand these continuous-time nonlinear filters (the distribution function and the sorting) and presents some of their properties in a tutorial way. The analog median filter is defined in terms of the (unique) nonincreasing left-continuous sorting. More general filters can also be defined, including filters similar to /spl alpha/-trimmed mean filters and L filters. These include filters that depend on one parameter and contain the running average and running median as special cases. The rate of convergence of the digital median filter to the analog median filter is discussed and related to the signal sampling period, the duration of the filter window, and the smoothness of the input signal. The paper introduces the concept of noise width and studies the effect of additive and multiplicative noise at the output of the analog median filter in terms of the noise width and the smoothness of the input signal.
Sponsorship	IEEE Signal Processing Society
Starting Page	2734
Ending Page	2744
Page Count	11
File Size	260334
File Format	PDF
ISSN	1053587X
Volume Number	49
Issue Number	11
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2001-11-01
Publisher Place	U.S.A.
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Sorting Additive noise Digital filters Nonlinear systems Statistics Delay lines Nonlinear filters Distribution functions Convergence Signal sampling
Content Type	Text
Resource Type	Article
Subject	Electrical and Electronic Engineering Signal Processing

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