Author: Jacques Gelinas, Ph.D., Maths, College Militaire Royal de Saint-Jean, Richelain, P. Quebec, Canada J0J 1R0.
Until June 1995: gelinas@cmr.ca
The daub package copmutes coefficients, values, moments, derivatives, antiderivatives, graphs of Daubechies scaling functions and wavelets in Maple V (1.1). All values can be computed to arbitrary precision by increasing the global variable Digits. The functions can be evaluated only at dyadic rational points of the form k/2^j, with k and j integers, but j can also be increased to yield a close approximation of the arguments. Precomputed (50d) coefficients of Daubechies low pass filters included.
Use it at your own risk... When 10 digits are printed for phi(4,2.1), this does not mean that all digits are correct (in fact, an argument like 2.1 is first converted to a dyadic rational k/2^Ndyad). However both the values of Digits and Ndyad can be increased to get more precision: in this sense the precision of the results of the daub package is arbitrary, a feature not found elsewhere.
One perfect application for daub is in teaching numerical analysis, where one can show on graphs the dilation equation, piece by piece:
> p := 2; c:=array( 0..2*p-1, daubc(p) );
> plot({ seq( sum(c[k]*phi(p,2*x-k),k=0..m), m=0..2*p-1) }, x=0..2*p-1);
daub Coefficients, values, graphs, moments, and (anti)derivatives of Daubechies scaling functions/wavelets in Maple V. (>?daub)
daubmac Macro definitions for all the global function names (not used).
daubut Accuracy estimation and refinement of approximations for the coefficients of Daubechies low pass filters. ( >?daubut )