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.