ABSTRACT
We begin with a new, self-contained development of the theory of Wilson bases. Wilson bases are modifications of the Gabor system which can be constructed to have good time and frequency localization. An example of a Wilson basis with compact support in time is given. After a review of Malvar (or Coifman and Meyer) bases, a general notion of local Fourier bases is presented. We show that this notion includes Wilson and Malvar bases.
