## Tuesday, December 15, 2015

### NCDF(S, 2, 2, L, 3): Example 2: S = [8, 7, 6, 5, 4, 3, 2, 1]

Problem

This post is a detailed example of computing individual elements of NCDF(S, 2, 2, L, 3) at each of the three scales on S = [8, 7, 6, 5, 4, 3, 2, 1]. NCDF(S, 2, 2, L, J) notation is defined here. This notation is based on the notation introduced in Chapters 3 and 4 in "Ripples in Mathematics" by A. Jensen & A. la Cour-Harbo.

NCDF(S, 2, 2, 1, 3): Scale L = 1

Figures 1 and 2 show the formulas for the elements of S and D at scale L = 1. Figure 3 shows an example of computing the first scale of the signal S = [8, 7, 6, 5, 4, 3, 2, 1].
 Figure 1. Formulas for individual elements of S at scale L = 1
 Figure 2. Formulas for individual elements of D at scale L = 1
 Figure 3. Computing individual elements of S and D at scale L = 1

NCDF(S, 2, 2, 2, 3): Scale L = 2

Figure 4 shows the individual formulas for S and D at scale L = 2. Figure 5 shows the computation of individual elements of S and D of the sample S = [8, 7, 6, 5, 4, 3, 2, 1]. at scale L = 2.
 Figure 4. Formulas for individual elements of S and D at scale L = 2
 Figure 5. Computing individual elements of S and D at scale L = 2

NCDF(S, 2, 2, 3, 3): Scale L = 3

Figure 6 shows the individual formulas for S and D at scale L = 3. Figure 7 shows the computation of individual elements of S and D of the sample S = [8, 7, 6, 5, 4, 3, 2, 1]. at scale L = 3.
 Figure 6. Formulas for individual elements of S and D at scale L = 3
 Figure 7. Computing elements of S and D at scale L = 3

Summary of NCDF(S, 2, 2, 3, 3) at All Three Scales

Figure 8 summarizes the three scales of NCDF(S, 2, 2, 3, 3), where S = [8, 7, 6, 5, 4, 3, 2, 1].

 Figure 8. Summary of NCDF(S, 2, 2, 3, 3) at all three scales on S = [8, 7, 6, 5, 4, 3, 2, 1]