## Abstract

Rank-order-based filters include rank-order filters, stack filters, and weighted order statistic filters. The output of a rank-order-based filter is always one of the sample points in its input window; which one is chosen depends only upon the ranks and positions of the samples within the window. This paper introduces new architectures for rank-order-based filters. They all achieve fast, efficient operation by exploiting an algorithm called input compression. Under this algorithm, the sample points in the input window are first mapped to their relative ranks - the sample points in a window of size N + 1 would thus be mapped to the integers 0-N. The rank-order-based filter to be implemented is then applied directly to this compressed input, and the rank chosen is then mapped back to the sample of that rank in the original data to obtain the final output. This approach has been used to implement rank-order filters, in which case the same rank is always chosen from the compressed data. In this paper, which rank is chosen also depends on the positions of the ranks in the compressed data. Implementations employing input compression have several advantages. They are computationally efficient like running order sorters, yet can be pipelined to a fine degree like sorting networks. In stack filter implementations, the threshold decomposition circuitry can be eliminated when input compression is combined with unary encoding of the ranks. Weighted order statistic filter implementations based on input compression can support programmable, noninteger weights.

Original language | English (US) |
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Pages (from-to) | 441-453 |

Number of pages | 13 |

Journal | Signal Processing |

Volume | 38 |

Issue number | 3 |

DOIs | |

State | Published - Aug 1994 |

### Bibliographical note

Funding Information:Die Klasse der Rank-Order-Filter schliesst sowohl die eigentlichen Rank-Order-Filter, die Stackfilter als auch gewichtete statistische Filter ein. Der Ausgabewert eines dieser Filter entspricht immer genau einem der Abtastwerte im Eingabefenster; welcher dieser Werte ausgew/ihlt wird, h/ingt dabei von der Ordnung und Position der Eingabewerte innerhalb des Fensters ab. Dieser Artikel stellt neue Architekturen fiir Rank-Order-Filter vor. Sie alle garantieren eine * Corresponding author. *T his research was supported in part by the National Science Foundation under grant EET87-21333, an AT&T graduate fellowship, and the Office of Naval Research under contract number N00014-91-J-1008.

## Keywords

- Input compression
- Rank-order filters
- Stack filters
- Unary encoded rank
- VLSI architecture
- Weighted order statistic filters