Coiflet
Coiflet is a discrete wavelet designed by Ingrid Daubechies to be more symmetrical than the Daubechies wavelet.
Coiflet coefficients
Both the Scaling Function (Low-Pass Filter) and the Wavelet Function (High-Pass Filter) must be normalised by a factor <math>\frac{1}{\sqrt{2}} <math>. Below are the coefficients for the scaling functions for C6–30. The wavelet coefficients are derived by reversing the order of the scaling function coefficients and then reversing the sign of every second one. (ie. C6 wavelet = {-0.022140543057, 0.102859456942, 0.544281086116, -1.205718913884, 0.477859456942, 0.102859456942}) Mathematically, this looks like <math> B_k = (-1)^{k} C_{N – 1 – k} <math> where k is the coefficient index, B is a wavelet coefficient and C a scaling function coefficient. N is the wavelet index, ie 6 for C6.
| k | C6 | C12 | C18 | C24 | C30 |
|---|---|---|---|---|---|
| 0 | -0.102859456942 | 0.023175193479 | -0.005364837341 | 0.001261922093 | -0.000000134600 |
| 1 | 0.477859456942 | -0.058640275960 | 0.011006253418 | -0.002304449705 | -0.000000236800 |
| 2 | 1.205718913884 | -0.095279180620 | 0.033167120958 | -0.010389048053 | 0.000002918600 |
| 3 | 0.544281086116 | 0.546042093070 | -0.093015528958 | 0.022724918488 | 0.000005281600 |
| 4 | -0.102859456942 | 1.149364787715 | -0.086441527120 | 0.037734470756 | -0.000030144000 |
| 5 | -0.022140543057 | 0.589734387392 | 0.573006670549 | -0.114928468858 | -0.000058464200 |
| 6 | -0.108171214184 | 1.122570513741 | -0.079305297034 | 0.000198755200 | |
| 7 | -0.084052960922 | 0.605967143547 | 0.587334781789 | 0.000427459600 | |
| 8 | 0.033488820325 | -0.101540281510 | 1.106252905125 | -0.000902454000 | |
| 9 | 0.007935767225 | -0.116392501524 | 0.614314652395 | -0.002351644400 | |
| 10 | -0.002578406712 | 0.048868188642 | -0.094225477729 | 0.003441309400 | |
| 11 | -0.001019010797 | 0.022458481925 | -0.136076254102 | 0.009566002800 | |
| 12 | -0.012739202022 | 0.055627280306 | -0.012960180000 | ||
| 13 | -0.003640917832 | 0.035471674876 | -0.027947375800 | ||
| 14 | 0.001580410202 | -0.021512637034 | 0.046221554000 | ||
| 15 | 0.000659330348 | -0.008002025773 | 0.058391759000 | ||
| 16 | -0.000100385550 | 0.005305331892 | -0.149304477801 | ||
| 17 | -0.000048931468 | 0.001791189058 | -0.087732101600 | ||
| 18 | -0.000833001142 | 0.619413698002 | |||
| 19 | -0.000367659537 | 1.095010858804 | |||
| 20 | 0.000088160707 | 0.596184647002 | |||
| 21 | 0.000044165714 | -0.073600147200 | |||
| 22 | -0.000004609884 | -0.129994525601 | |||
| 23 | -0.000002524350 | 0.039835608600 | |||
| 24 | 0.033104132800 | ||||
| 25 | -0.014327563800 | ||||
| 26 | -0.005882221600 | ||||
| 27 | 0.003080491400 | ||||
| 28 | 0.000507122400 | ||||
| 29 | -0.000299927600 |
It needs more information about how the coefficients are derived. This set is not the only solution to the deriving equations.
Categories: Mathematics stubs | Wavelets