Moving Average and Savitzki-Golay Smoothing Filters Using Mathcad

Abstract

All measurement processes cause certain amount of random variations in the signal; this phenomenon is called noise. The procedure to reduce or smooth the noise of a measured signal is commonly known as filtering. In this paper we present the us e of Mathcad software for the implementation and analysis of the moving average and Savitzky-Golay filters. The moving average filter is the simplest digital filte r to understand and use. As its name suggests, this filt er operates by averaging a number of points in a recur sive fashion. In spite of its simplicity, the moving ave rage filter is effective for time domain encoded signals . The Saviztky-Golay filter is based on the least squares polynomial fitting across a moving window within the data in the time domain. Generally, a high order polynomial (n=4) allows a high level of smoothing without attenuation of data features. By contrast, the Saviztky-Golay filtering method is better than aver aging because it tends to preserve data features such as peak height and width, which are usually attenuated by t he moving average filter. By means of the Mathcad software, moving average and Savitzky-Golay filters were successfully applied to the smoothing of photochemical and electrochemical reactor data.