2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/101218A generalized filter construction is used to build an example of a non-MRA normalized tight frame wavelet for dilation by 2 in $L^2(\mathbb R)$. This example has the same multiplicity function as the Journé wavelet, yet has a $C^{\infty}$ Fourier transform and can be made to be $C^r$ for any fixed positive integer $r$.20 pages; v2 has graphics for Figures 1, 2, 3, 4; v3 has Figures 5, 6; accepted in 'Acta Applicandae Mathematicae'Classical Analysis and ODEsOperator Algebras54C40, 14E20 (Primary), 46E25, 20C20 (Secondary)text