On the digital filter associated with Daubechies' wavelets

|The magnitude of the lters associated with Daubechies' wavelets is shown to converge to an ideal high-pass lter when the length of the support of the wavelets increases to 1. The convergence of the lters is monotonic. That is, the larger support of a Daubechies' wavelet, the better quality of the lter associated with. The rate of the convergence is also given. The magnitude of the lter associated with each Daubechies' wavelet is shown to be monotonically increasing from 0; ]. Finally, the approximation to the ideal high-pass lter does not have Gibbs' phenomenon.