Some results on product-function frames

This paper introduces the concept of product function frames. These frames are a collection of sequences, or frame kernels, that are represented as pr oducts of two or more sequences. This forms a generalized structure for man y of the currently existing transforms. We define the conditions on the fra me and dual frame kernels for the space of periodic discrete-time sequences . We then derive windowed transforms, modulated filterbanks, and oversample d filterbanks as special cases. Finally, we introduce a new family of trans forms, which we call 'product transforms'. (C) 2000 Published by Elsevier S cience B.V. All rights reserved.