Smoothing methods

The interpolation method outlined above can be applied as well to the "smoothing of experimental data. In this case a given experimental point is replaced by a point whose position is calculated from the values of m points on each side. The matrix X then contains an odd number of columns, namely 2m + 1. The matrices A have also been tabulated for this application. This smoothing method has been used for a number of years by molecular spectroscopists, who generally refer to it as the method of Savitzky and Golay. ... 

Tills method works reasonably well for general smoothing. Use if no better smoothing methods arc available. 

To improve the accuracy of e, a data smoothing method such as a moving average is applied to the measured data as required. 

The moving average is a process similar to exponential smoothing. The exponential smoothing method (see also Section 6.4.2) has exponentially decreasing coefficients of the recent values. In a MA model the single coefficients b1 b2,. .., b were calculated by minimization of the sum of squared errors. 

This attenuation can be made by smoothing methods that allow data extrapolation, if the number of experimental points is reduced. The smoothing methods should also allow rate calculation from these points. The most commonly used smoothing techniques of experimental data are presented below. 

More often the data-enhancement step is done later, to simplify the data processing and to lower the computational burden placed on the instrumental computer. When data are enhanced either at-line or off-line, after data acquisition is complete, the process is called smoothing. Smoothing methods are much more varied than ones used exclusively for filtering because the time and computational constraints are not as demanding. It should be noted, however, that most filtering methods can also be used for smoothing. 

Problem 3.5 Some Simple Smoothing Methods for Time Series... 

Standard baseline subtraction and smoothing methods are applied to each individual MALDI spectrum after measurement or on-the-fly during acquisition in order to reduce the influence of chemical noise (Figure 2D) (35). While this is performed independently on each mass spectrum, other processing steps such as normalization, recalibration, and peak picking have to account for the large number of individual spectra in MSI data. 

Minitab computes three measures of accuracy of the fitted model MAPE, MAD, and MSD for each of the simple forecasting and smoothing methods. For all three measures, the smaller the value, the better the fit of the model. These statistics are used to compare the fits of the different methods. 

In addition to the smoothing methods based on digital filters and on transformations, some further possibilities exist for signal smoothing. Among these are the following ... 

Brown s ejqtonential smoothing method is used for forecasting time series data that have a linear trend. This method is similar to double moving average techniques. Only one smoothing constant is used in this method. 

Holt s two-parameter linear-exponential smoothing method is used to smooth trend and slope directly by using different smoothing constants for each. Using two constants gives more flexibility in selecting rates at which trend and slope can be followed. 

ES Agent, finally, determines forecasts according to the simple exponential smoothing method, which estimates the demand in any period as the weighted average of the last period demand and the forecast of demand in that period. It can be expressed... 

The predictive results of cubic exponential smoothing method... 

Liu Yang Ma Fenghai. 2007. Application of cubic exponential smoothing method to city underground deformation prediction. Technology Economy in Areas of Communicatitms (5) 62-70. 

Zhu Qingming Hao Zhang. 2012. Study on the application of cubic exponential smoothing method in coal mine accidents forecasting. Joural of Safety Science and Technology (4) 105-107. 

Zhang Weihong Li liu. 2008. Application of exponential smoothing method in the sales budget. China Management Information (2) 85-86. 

The weighted smoothing method tries to find a compromise between the two contradictory requirements of high smoothness and low smoothing error. This compromise is controlled via an additional weighting parameter X > nd the following constrained minimization problem is solved ... 

The simplest smoothing method uses a uniform weighting of adjacent channels. That is, y, the smoothed value for the counts in channel x, is obtained from adjacent channels by... 

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