Coiflet

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 $N/3$. They are named in honor of Ronald Coifman, who first requested them.

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 $B_{k}=(-1)^{k}C_{N-1-k}$ 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