Geodesic
Refinement masks of tight wavelet frames
Zapiski Nauchnykh Seminarov POMI, Investigations on applied mathematics and informatics. Part I, Tome 499 (2021), pp. 53-66

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In the paper we obtain sufficient conditions for a trigonometric polynomial to be a refinement mask corresponding to a tight wavelet frame. The condition is formulated in terms of the roots of a mask. In particular, it is proved that any trigonometric polynomial can serve as a mask if its associated algebraic polynomial has only nonpositive roots (at least one of them, of course, equals $-1$). 
@article{ZNSL_2021_499_a4,
     author = {E. A. Lebedeva and I. A. Sherbakov},
     title = {Refinement masks of tight wavelet frames},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {53--66},
     publisher = {mathdoc},
     volume = {499},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2021_499_a4/}
}
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E. A. Lebedeva; I. A. Sherbakov. Refinement masks of tight wavelet frames. Zapiski Nauchnykh Seminarov POMI, Investigations on applied mathematics and informatics. Part I, Tome 499 (2021), pp. 53-66. http://geodesic.mathdoc.fr/item/ZNSL_2021_499_a4/