Moving window average

The simplest smoothing procedure is a moving window average, in which each of 2N data points is replaced by the mean of itself and its nearest neighbours ... 

The distributions of (R)tw obtained for a polypeptide immobilized on the attractive surface are presented in Fig. 11. Surface-immobilization is seen once again not to affect the behavior of the folded state. In this case, surface immobilization is also seen to have a relatively minor effect on the behavior at the midpoint. However, the behavior in unfolded states a and fi is clearly influenced by surface immobilization in this case. More specifically, the (R)tw distributions are hardly affected by the time-window-averaging for values of Tw that were seen to significantly modify the (R)tw distributions in the freely diffusing and repulsive surface-immobilized cases. This can be attributed to the slower dynamics of the unfolded polypeptide on the attractive surface. At the same time, conformations with a small value of R are still seen to move faster than conformations with a large value of R, as for the freely diffusing polypeptide. 

Comparison of Equations (2.25) and (2.28) makes it readily apparent that Agb(/) and Lc are fundamentally different concepts, even though they are both referred to as lacunarities. Indeed, whereas Agb(/) depends on the side length / of the moving windows or structuring element, Chappard et al. s [46] lacunarity Lc does not depend on /, as a result of the averaging of cv(/) over the number of circle radii k in... 

For the purpose of hypothesis testing (Fisher 1930 Romano 2005), the residuals r t) are averaged over a moving window and the mean (/x) is subjected to a hypothesis test at a chosen significance level a, as follows ... 

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

An example is the relatively simple moving average filter. In case of a digitized signal, the values of a fixed (odd) number of data points (a window) are added and divided by the number of points. The result is a new value of the center point. Then the window shifts one point and the procedure, which can be considered as a convolution of the sipal with a rectangular pulse function, repeats. Of course, other functions like a triangle, an exponential and a Gaussian, can be used. 

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