Periodic wavelet frames and time–frequency localization

•A family of Parseval periodic wavelet frames is constructed.•The family has minimal uncertainty constant with respect to a family parameter.•The family has the best currently known localization with respect to a MRA parameter.•The family is constructed using a nonstationary periodic MRA.

A family of Parseval periodic wavelet frames is constructed. The family has optimal time–frequency localization (in the sense of the Breitenberger uncertainty constant) with respect to a family parameter and it has the best currently known localization with respect to a multiresolution analysis parameter.