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 1/\sqrt{2} . 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.

Coiflets coefficients
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