Accounting For Order-Frame Length Tradeoff of Savitzky-Golay Smoothing Filters

Abstract

Pre-processing techniques such as filtering and smoothing techniques play crucial role in better interpretation of the signal. There are numerous filters viz. median, band-pass, notch and smoothing filters viz. moving average, Savitzky-Golay for removing the unwanted noise signals from the original signal. These techniques are a boon if they reduce the noise from the signal while preserving its morphology. One of the filters, Savitzky-Golay (SG) filter has this property and is extensively used in smoothing a number of biomedical signals viz. Electroencephalogram (EEG), Electrocardiogram (ECG). The better performance of SG filters lead to the cascading of these filters to provide much better results. The cascading no doubt proved more efficient in keeping the signal structure intact but the number of stages up to which cascading can work efficiently is not known. A SG smoothing filter depends upon the randomly chosen order and frame length for its application. A suitable value from the set of random values is determined which outperforms other values. The value chosen is just through a hit-and-trial procedure but not with any significant algorithm. Therefore, the aim of the present work is to find: (i) the optimum value up to which Savitzky-Golay filters can be cascaded (ii) effect of order and frame length on cascading and choosing the optimum value of these parameters for optimum filter design.