Brody Dylan Johnson

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Motivated by the notion of orthogonal frames, we describe sufficient conditions for the construction of orthogonal MRA wavelet frames in L 2 (R) from a suitable scaling function. These constructions naturally lead to filter banks in 2 (Z) with similar orthogo-nality relations and, through these filter banks, the orthogonal wavelet frames give rise to a(More)
This paper explores the dimensionality of responses to the Adult Behavior Checklist Revised, a screening assessment for Attention Deficit Hyperactivity Disorder (ADHD) in college students, and demonstrates a standard setting process for diagnostic rating scales. Responses from 317 undergraduate college students were used to investigate dimensionality; 8(More)
This article continues a prior investigation of the authors with the goal of extending characterization results of convolutional tight frames from the context of cyclic groups to general finite abelian groups. The collections studied are formed by translating a number of generators by elements of a fixed subgroup and it is shown, under certain norm(More)
The properties of oversampled affine frames are considered here with two main goals in mind. The first goal is to generalize the approach of Chui and Shi to the matrix oversampling setting for expanding, lattice-preserving dilations, whereby we obtain a new proof of the Second Oversampling Theorem for affine frames. The Second Oversampling Theorem, proven(More)
Acknowledgments I am fully indebted to my two advisors, Guido Weiss and Ed Wilson. Our frequent meetings in Guido's office have been truly rewarding mathematically and personally. They have been excellent teachers, compassionate critics, timely superiors, and generous friends. Their mentorship has only been surpassed by their obvious concern for me as a(More)