In the present paper, Daubechies' wavelets and the computation of their scaling coefficients are briefly reviewed. Then a new method of computation is proposed. This method is based on the work  concerning a new orthonormality condition and relations among scaling moments, respectively. For filter lengths up to 16, the arising system can be explicitly solved with algebraic methods like Gröbner bases. Its simple structure allows one to find quickly all possible solutions.
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