ABSTRACT
Local trigonometric bases consist of cosines and sines multiplied by smooth, well-localized window functions in order to have basis functions with good time-frequency localization. On the one hand, bases in the two-overlapping setting are considered. In particular, the development of such bases from the orthonormal bases of Coifman and Meyer to the general approach for the construction of biorthogonal bases introduced by Chui and Shi is reviewed. On the other hand, a new generalized theory for biorthogonal Wilson bases is presented which includes former approaches. Connections between the two-overlapping bases and the Wilson bases are pointed out. Numerous examples illustrate the theoretical results.
