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Proceedings Paper

A comparison of noise removal by the Fourier and the Haar transformations
Author(s): Chang-Hsin Kuo; Jhy-Cherng Tsai; Yi-Ji Chen
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Paper Abstract

This paper compared noise removal using the Fourier series and the Haar wavelet transformations. The results showed that noise from the measured data can be filtered by neglecting high-order terms of Fourier coefficients. It also showed that signal denoising can be achieved by Haar wavelet transformation by filtering the noise before inverting the transformed data back to time domain. A further comparison using a set of data with variation 6.3mV from five measurements of a sample showed that the variations after denoising can be reduced to 3.8mV by the Fourier series and to 2.3mV by 3-level Haar wavelet. Both methods can filter noise in signal and keep the predicted curve consistent with the measured data. The signal becomes smooth if denoised by the Fourier series but the variation of signal, however, can be reduced more if denoised by the Haar wavelet. Moreover, from the computation complexity viewpoint, signal denoising by Haar wavelet is much better than that by Fourier series.

Paper Details

Date Published: 15 November 2011
PDF: 10 pages
Proc. SPIE 8321, Seventh International Symposium on Precision Engineering Measurements and Instrumentation, 83213Y (15 November 2011); doi: 10.1117/12.905636
Show Author Affiliations
Chang-Hsin Kuo, National Chung-Hsing Univ. (Taiwan)
Hiwin Technologies Co., Ltd. (Taiwan)
Jhy-Cherng Tsai, National Chung-Hsing Univ. (Taiwan)
Yi-Ji Chen, National Chung-Hsing Univ. (Taiwan)

Published in SPIE Proceedings Vol. 8321:
Seventh International Symposium on Precision Engineering Measurements and Instrumentation
Kuang-Chao Fan; Man Song; Rong-Sheng Lu, Editor(s)

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