Authors
Sunder Ram Krishnan, Chandra Sekhar Seelamantula
Publication date
2012/10/16
Journal
IEEE transactions on signal processing
Volume
61
Issue
2
Pages
380-391
Publisher
IEEE
Description
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 …
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Scholar articles
SR Krishnan, CS Seelamantula - IEEE transactions on signal processing, 2012