1 Applied functional analysis, Department of Mathematics, Technical University of Denmark2 Department of Mathematics, Technical University of Denmark3 Department of Applied Mathematics and Computer Science, Technical University of Denmark
For sufficiently small translation parameters, we prove that any bandlimited function ψ, for which the dilations of its Fourier transform form a partition of unity, generates a wavelet frame with a dual frame also having the wavelet structure. This dual frame is generated by a finite linear combination of dilations of ψ with explicitly given coefficients. The result allows a simple construction procedure for pairs of dual wavelet frames whose generators have compact support in the Fourier domain and desired time localization. The construction is based on characteriszing equations for dual wavelet frames and relies on a technical condition. We exhibit a general class of function satisfying this condition; in particular, we construct piecewise polynomial functions satisfying the condition.
partition of unity; non-tight frames; dual frames; wavelet; framelets