Coiflet
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Coiflet is a discrete wavelet designed by Ingrid Daubechies to be more symmetrical than the Daubechies wavelet. Whereas Daubechies wavelets have N / 2 − 1 vanishing moments, Coiflet scaling functions have N / 3 − 1 zero moments and their wavelet functions have N / 3.
[edit] Coiflet coefficients
Both the scaling function (low-pass filter) and the wavelet function (High-Pass Filter) must be normalised by a factor 
. 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 Bk = ( − 1)kCN − 1 − k 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 |
