Brody Dylan Johnson

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Abstract. 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(More)
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(More)
Motivated by the notion of orthogonal frames, we describe sufficient conditions for the construction of orthogonal MRA wavelet frames in L(R) from a suitable scaling function. These constructions naturally lead to filter banks in `(Z) with similar orthogonality relations and, through these filter banks, the orthogonal wavelet frames give rise to a(More)
Motivated by recent developments in the study of finitedimensional frames, this work develops an independent theory of finitedimensional wavelet systems on the circle. Using natural translation and dilation operators, trigonometric polynomial, orthonormal scaling functions are constructed which give rise to finite-dimensional multiresolution analyses and,(More)
In recent years, hybrid absorption systems have been implemented which achieve high sound absorption over a broad frequency range. This work is an experimental study of a broadband hybrid absorption system which is comprised of a layer of sound-absorbing material ~the passive component! positioned at a distance from a movable wall ~the active component!(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 relationship between multiresolution analysis and filtering schemes is a well-known facet of wavelet theory. However, in the case of rational dilation factors, the wavelet literature is somewhat lacking in its treatment of this relationship. This work seeks to establish a means for the construction of stable filtering schemes with rational dilations(More)
An old problem in the field of holonomy asks: Given a pair of orientations for a sphere resting on a plane, is there a closed path along which one can roll the sphere (without slipping or twisting), starting with the first orientation, and return to the origin with the sphere in the second orientation? (See Figure 1.) The answer is yes, and the goal of this(More)