Moving average smoothing

The errors of any functional relationships may be such moving average processes. Then these errors depend not only on the goodness of fit at time t but also on the goodness of fit from recent estimations because of the moving average smoothing function. 

Problem 3.1 Savitsky-Golay and Moving Average Smoothing Functions... 

FIGURE 5-13 The operation of an unweighted moving average smoothing function noisy spectral data ( ). smoothed data (A). See lexl for a description of the smoothing procedure. 

Running Average Smoothing n An alternate term for moving average smoothing. 

Another approach to smoothing is to use the arithmetic moving average, which is represented by the following equation ... 

Figure 3.11. Smoothing a noisy signal. The synthetic, noise-free signal is given at the top. After the addition of noise by means of the Monte Carlo technique, the panels in the second row are obtained (little noise, left, five times as much noise, right). A seven-point Savitzky-Golay filter of order 2 (third row) and a seven-point moving average (bottom row) filter are...

Fig. 40.22. Distortion (hJhn) of a Gaussian peak for various window sizes (indicated within parentheses). (a) Moving average, (b) Polynomial smoothing.

The convolution or smoothing function, h f), used in moving averaging is a simple block function. However, one could try and derive somewhat more complex convolution functions giving a better signal-to-noise ratio with less deformation of the underlying deterministic signal. 

For an IIR filter, the parameter T in Eq. (9) tends to infinity. IIR filters can be represented as a function of previous filter outputs and often can be computed with fewer multiplications and reduced data storage requirements compared to a FIR filter. A popular example of an IIR filter is the exponentially weighted moving average (EWMA) or exponential smoothing, which is represented as... 

Smoothing At this stage, noise was still present and resulted in small but very fast and short changes. The scores then were smoothed with a 5-point moving average. 

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

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