A comparison of noise removal by the Fourier and the Haar transformations

Chang-Hsin Kuo; Jhy-Cherng Tsai; Yi-Ji Chen

doi:10.1117/12.905636

15 November 2011 A comparison of noise removal by the Fourier and the Haar transformations

Chang-Hsin Kuo, Jhy-Cherng Tsai, Yi-Ji Chen

Proceedings Volume 8321, Seventh International Symposium on Precision Engineering Measurements and Instrumentation; 83213Y (2011) https://doi.org/10.1117/12.905636
Event: Seventh International Symposium on Precision Engineering Measurements and Instrumentation, 2011, Yunnan, China

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.

Citation Download Citation

Chang-Hsin Kuo, Jhy-Cherng Tsai, and Yi-Ji Chen "A comparison of noise removal by the Fourier and the Haar transformations", Proc. SPIE 8321, Seventh International Symposium on Precision Engineering Measurements and Instrumentation, 83213Y (15 November 2011); https://doi.org/10.1117/12.905636

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KEYWORDS

Wavelets

Interference (communication)

Denoising

Sensors

Wavelet transforms

Electronic filtering

Filtering (signal processing)

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