On the Selection of Optimum Savitzky-Golay Filters

Krishnan, Sunder Ram and Seelamantula, Chandra Sekhar (2013) On the Selection of Optimum Savitzky-Golay Filters. In: IEEE TRANSACTIONS ON SIGNAL PROCESSING, 61 (2). pp. 380-391.

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Abstract

Savitzky-Golay (S-G) filters are finite impulse response lowpass filters obtained while smoothing data using a local least-squares (LS) polynomial approximation. Savitzky and Golay proved in their hallmark paper that local LS fitting of polynomials and their evaluation at the mid-point of the approximation interval is equivalent to filtering with a fixed impulse response. The problem that we address here is, ``how to choose a pointwise minimum mean squared error (MMSE) S-G filter length or order for smoothing, while preserving the temporal structure of a time-varying signal.'' We solve the bias-variance tradeoff involved in the MMSE optimization using Stein's unbiased risk estimator (SURE). We observe that the 3-dB cutoff frequency of the SURE-optimal S-G filter is higher where the signal varies fast locally, and vice versa, essentially enabling us to suitably trade off the bias and variance, thereby resulting in near-MMSE performance. At low signal-to-noise ratios (SNRs), it is seen that the adaptive filter length algorithm performance improves by incorporating a regularization term in the SURE objective function. We consider the algorithm performance on real-world electrocardiogram (ECG) signals. The results exhibit considerable SNR improvement. Noise performance analysis shows that the proposed algorithms are comparable, and in some cases, better than some standard denoising techniques available in the literature.

Item Type:	Journal Article
Publication:	IEEE TRANSACTIONS ON SIGNAL PROCESSING
Publisher:	IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
Additional Information:	Copyright for this article belongs to IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, USA
Keywords:	Bias;local polynomial regression;MMSE;Savitzky-Golay filters;Stein's lemma;SURE;variance
Department/Centre:	Division of Electrical Sciences > Electrical Engineering
Date Deposited:	09 Mar 2013 07:16
Last Modified:	09 Mar 2013 07:16
URI:	http://eprints.iisc.ac.in/id/eprint/46005

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