Causal equivalence of frames [electronic resource] /
Abstract (Summary)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.
School Location:USA - Texas
Source Type:Master's Thesis
Keywords:major mathematics bases gram schmidt frames
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