Critical Exponent of Short Even Filters andBurt-Adelson Biorthogonal Wavelets

 We determine the critical exponent of all positive filters having an even residual of degree two and present an extension to the case of degree four. We apply these results to Burt-Adelson filters, thus determining the critical exponent of all the biorthogonal wavelets they generate. After this, we consider the problem of smoothing the dual wavelets by considering longer dual filters: we first create new wavelets by imposing an extra zero at π on the new filters and study their regularity by determining all the critical exponents. Then we release this condition on the filters and present the results of a numerical simulation intended to maximize the Sobolev regularity. (Received 10 February 2000; in revised form 16 May 2000)