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Robust Savitzky-Golay Filters

Menon, Sreeram V and Seelamantula, Chandra Sekhar (2014) Robust Savitzky-Golay Filters. In: 19th International Conference on Digital Signal Processing (DSP), AUG 20-23, 2014, Hong Kong, PEOPLES R CHINA, pp. 688-693.

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Local polynomial approximation of data is an approach towards signal denoising. Savitzky-Golay (SG) filters are finite-impulse-response kernels, which convolve with the data to result in polynomial approximation for a chosen set of filter parameters. In the case of noise following Gaussian statistics, minimization of mean-squared error (MSE) between noisy signal and its polynomial approximation is optimum in the maximum-likelihood (ML) sense but the MSE criterion is not optimal for non-Gaussian noise conditions. In this paper, we robustify the SG filter for applications involving noise following a heavy-tailed distribution. The optimal filtering criterion is achieved by l(1) norm minimization of error through iteratively reweighted least-squares (IRLS) technique. It is interesting to note that at any stage of the iteration, we solve a weighted SG filter by minimizing l(2) norm but the process converges to l(1) minimized output. The results show consistent improvement over the standard SG filter performance.

Item Type: Conference Proceedings
Series.: International Conference on Digital Signal Processing
Publisher: IEEE
Additional Information: Copy right for this article belongs to the IEEE, 345 E 47TH ST, NEW YORK, NY 10017 USA
Keywords: Savitzky-Golay filters; Finite impulse response; Mean-squared error; Iteratively reweighted least-squares technique
Department/Centre: Division of Electrical Sciences > Electrical Engineering
Date Deposited: 09 Oct 2015 05:54
Last Modified: 09 Oct 2015 05:54
URI: http://eprints.iisc.ac.in/id/eprint/52528

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