Colloquium 12/5: Discrete Fourier Analysis and New Circulant Weighing Matrices

On Monday December 5^th at 3:30, Dr. Ken Smith will be giving a talk titled “Discrete Fourier Analysis and New Circulant Weighing Matrices.” This should be an interesting and accessible talk for all.

Abstract:

A circulant weighing matrix CW(n,k) is a square n x n matrix M with entries from {-1, 0, 1} such that MM* = kI. (Here M* is the transpose matrix and I is the n x n identity matrix.) Circulant weighing matrices have applications to signal processing and digital communications. Using techniques in “discrete Fourier analysis” and algebraic number theory, we construct a circulant weighing matrix with parameters CW(48,36). Such a matrix was conjectured not to exist. The techniques used in this construction are those of a first-year graduate class in higher algebra and should be accessible to a broad audience. (This is joint work with Bernhard Schmidt, Nanying Technological University, Singapore.)