Sufficient conditions for a trigonometric polynomial to be refinement mask corresponding tight wavelet frame are obtained. The condition is formulated in terms of the roots mask. In particular, it proved that any can serve as if its associated algebraic has only negative (of course at least one them equals −1).

This work characterizes (dyadic homogeneous) wavelet frames for $$L^2({{\mathbb {R}}})$$ by means of spectral techniques. These techniques use decomposability properties the frame operator in representations associated with dilation operator. The approach is closely related to usual Fourier domain fiberization techniques, dual Gramian analysis, and extension principles. Spectral formulas are us...