Design of linear combination of weighted medians

Kang Sun Choi, Aldo W. Morales, Sung Jea Ko

Research output: Contribution to journalArticlepeer-review

23 Scopus citations


This paper introduces a novel nonlinear filtering structure: the linear combination of weighted medians (LCWM). The proposed filtering scheme is modeled on the structure and design procedure of the linear-phase FIR highpass (HP) filter in that the linear-phase FIR HP filter can be obtained by changing the sign of filter coefficients of the FIR lowpass (LP) filter in the odd positions. The HP filter can be represented as the difference between two LP subfilters that have all positive coefficients. This representation of the FIR HP filter is analogous to the difference of estimates (DoE) such as the difference of medians (DoM). The DoM is essentially a nonlinear HP filter that is commonly used in edge detection. Based on this observation, we introduce a class of LCWM filters whose output is given by a linear combination of weighted medians of the input sequence. We propose a method of designing the 1-D and 2-D LCWM filters satisfying required frequency specifications. The proposed method adopts a transform ation from the FIR filter to the LCWM filter. We show that the proposed LCWM filter can offer various frequency filtering characteristics including "LP," "bandpass (BP)," and "HP" responses.

Original languageEnglish (US)
Pages (from-to)1940-1952
Number of pages13
JournalIEEE Transactions on Signal Processing
Issue number9
StatePublished - Sep 2001

All Science Journal Classification (ASJC) codes

  • Signal Processing
  • Electrical and Electronic Engineering


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