Causal equivalence of frames
Abstract
Frames have recently become popular in the area of applied mathematics known
as digital signal processing. Frames offer a level of redundancy that bases do not
provide. In a sub-area of signal processing known as data recovery, redundancy has
become increasingly useful; therefore, so have frames. Just as orthonormal bases are
desirable for numerical computations, Parseval frames provide similar properties as
orthonormal bases while maintaining a desired level of redundancy. This dissertation
will begin with a basic background on frames and will proceed to encapsulate my
research as partial fulfillment of the requirements for the Ph.D. degree in Mathematics
at Texas A&M University. More specifically, in this dissertation we investigate an
apparently new concept we term causal equivalence of frames and techniques for
transforming frames into Parseval frames in a way that generalizes the Classical Gram-
Schmidt process for bases. Finally, we will compare and contrast these techniques.
Citation
Henderson, Troy Lee, IV (2005). Causal equivalence of frames. Doctoral dissertation, Texas A&M University. Texas A&M University. Available electronically from https : / /hdl .handle .net /1969 .1 /4392.