This presentation is inspired from the Daubechies classic, "Ten Lectures on Wavelets", SIAM, 1992.

Daubechies gives the following result:

Hence can easily be found. There remains to find h. Observe that is symmetric with respect to the pulsation. Daubechies uses then the spectral factorization theorem:

which leads to h.

The "classical" Daubechies filters are such that R=0; in the spectral factorization, only the zeroes within the unit circle are kept.