Convolutional frames and the frame potential
نویسندگان
چکیده
The recently introduced notion of frame potential has proven useful for the characterization of finite-dimensional tight frames. The present work represents an effort to similarly characterize finite-dimensional tight frames with additional imposed structure. In particular, it is shown that the frame potential still leads to a complete description of tight frames when restricted to the class of translation-invariant systems. It is natural to refer to such frames as convolutional because of the correspondence between translation-invariant systems and finite-dimensional filter banks. The fast algorithms associated with convolution represent one possible advantage over non-convolutional frames in applications.
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