Wavelet interval-tree of scale

Fig, 13. Wavelet interval-tree of scales for the signal of Fig. 1 (a) extrema in shaded region reconstruct stable trend at m = 3 (see Fig. 

The wavelet interval-tree of scale is constructed fi om log 2 N distinct representations, where N is the number of points in the record of measured data. This is a far more efficient representation than that of scale-space filtering with continuous variation of Gaussian a. 

Step 2. Generate the wavelet interval-tree of scale. 

In Section II we defined the trend of a measured variable as a strictly ordered sequence of scaling episodes. Since each scaling episode is defined by its bounding inflexion points, it is clear that the extraction of trends necessitates the localization of inflexion points of the measured variable at various scales of the scale-space image. Finally, the interval tree of scale (see Section II) indicates that there is a finite number of distinct sequences of inflexion points, implying a finite number of distinct trends. The question that we will try to answer in this section is, How can you use the wavelet-based decomposition of signals in order to identify the distinct sequences of inflexion points and thus of the signal s trends ... 

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