Chapter 20 A Short Course on Frame Theory
ETH Zurich, Switzerland
Hilbert spaces [1, Def. 3.1–1] and the associated concept of orthonormal bases are of fundamental importance in signal processing, communications, control, and information theory. However, linear independence and orthonormality of the basis elements impose constraints that often make it difficult to have the basis elements satisfy additional desirable properties. This calls for a theory of signal decompositions that is flexible enough to accommodate decompositions into possibly nonorthogonal and redundant signal sets. The theory of frames provides such a tool.
This chapter is an introduction to the theory of frames, which was developed ...
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