title: |
Statistical analysis of a smoothing filter based on fuzzy transform |
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publication: |
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part of series: |
Advances in Intelligent Systems Research | |
| pages: | 472 - 479 | |
DOI: |
To be assigned soon (how to use a DOI) | |
author(s): |
Michal Holcapek, Tom¨¢s Tichy |
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publication date: |
July 2011 |
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keywords: |
Fuzzy transform, smoothing filter, statistical analysis, white noise reduction |
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abstract: |
The paper is devoted to the smoothing of discrete
functions using the fuzzy transform (shortly, Ftransform) introduced by Perfilieva in [1]. We generalize a smoothing filter based on the fuzzy transform proposed in [2] to obtain a better control on
the smoothed functions. For this purpose, a generalization of the concept of fuzzy partition is suggested
and the smoothing filter is defined as a combination of the direct discrete F-transform and a slightly
modified inverse continuous F-transform. Statistical properties including the description of the white
noise reduction and the asymptotic expression of
Bias and Var are investigated and discussed. |
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copyright: |
©
Atlantis Press. This article is distributed under the
terms of the Creative Commons Attribution License, which permits
non-commercial use, distribution and reproduction in any medium,
provided the original work is properly cited. |
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full text: |