We show that the compactly supported wavelet functions W-2, W-4, W-6,
discovered by Daubechies [6] can be computed by weighted finite automa
ta (WFA) introduced by Culik and Karhumaki [2]. Furthermore, for 1-D c
ase, a fixed WFA with 2(n) + n(N - 2) states can implement any linear
combination of dilations and translations of a basic wavelet W-N at re
solution 2(n). The coefficients of the wavelet transform specify the i
nitial weights in the corresponding states of the WFA, An algorithm to
simplify this WFA is presented and can be employed to compress data.
It works especially well for smooth and fractal-like data.