**Problem**

This
post is a detailed example of computing individual elements of SCDF(S,
2, 2, L, 3) at each of the three scales on S = [8, 7, 6, 5, 4, 3, 2, 1]. SCDF(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.

**SCDF(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 elements of S at scale L = 1 |

Figure 2. Formulas for elements of D at scale L = 1 |

Figure 3. Computing elements of S and D at scale L = 1 |

**SCDF(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 [8, 7, 6, 5, 4, 3, 2, 1] at scale L = 2.

Figure 4. Formulas for elements of S and D at scale L = 2 |

Figure 5. Computing elements of S and D at scale L = 2 |

**SCDF(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 [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 SCDF(S, 2, 2, 3, 3) at All Three Scales**

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

Figure 8. Computing three scales of SCDF(S, 2, 2, 3, 3) for S = [8, 7, 6, 5, 4, 3, 2, 1] |