7 papers
Cross-Correlation Periodograms with Decaying Noise Floor for Power Spectral Density Estimation
Mark Magsino
We present a statistical analysis of a variant of the periodogram method that forms power spectral density estimates by cross-correlating the discrete Fourier transforms of adjacen…
A Nonlinear Sum of Squares Search for CAZAC Sequences
Mark Magsino, Yixin Xu
We report on a search for CAZAC sequences by using nonlinear sum of squares optimization. Up to equivalence, we found all length 7 CAZAC sequences. We obtained evidence suggesting…
Biangular Gabor frames and Zauner's conjecture
Mark Magsino, Dustin G. Mixon
Two decades ago, Zauner conjectured that for every dimension , there exists an equiangular tight frame consisting of vectors in . Most progress to date expli…
Linear programming bounds for cliques in Paley graphs
Mark Magsino, Dustin G. Mixon, Hans Parshall
The Lovász theta number is a semidefinite programming bound on the clique number of (the complement of) a given graph. Given a vertex-transitive graph, every vertex belongs to a ma…
Kesten-McKay law for random subensembles of Paley equiangular tight frames
Mark Magsino, Dustin G. Mixon, Hans Parshall
We apply the method of moments to prove a recent conjecture of Haikin, Zamir and Gavish (2017) concerning the distribution of the singular values of random subensembles of Paley eq…
A Delsarte-Style Proof of the Bukh-Cox Bound
Mark Magsino, Dustin G. Mixon, Hans Parshall
The line packing problem is concerned with the optimal packing of points in real or complex projective space so that the minimum distance between points is maximized. Until recentl…
Constructing Tight Gabor Frames Using CAZAC Sequences
Mark Magsino
The construction of finite tight Gabor frames plays an important role in many applications. These applications include significant ones in signal and image processing. We explore w…