Abstract:Spectral estimation is an area of research within signal processing concerned with determining the frequencies of a signal based on finite uniform samples disrupted by noise. There exists a family of highly celebrated spectral estimation algorithms referred to as subspace methods which are widely known and readily available to the general public. Root-MUSIC is one such algorithm that approximates the signal's frequencies by constructing a high-degree polynomial and finding a subset of roots which are closest to the complex unit circle. We prove that the selection process chooses the relevant roots of the polynomial, and provide sharp, non-asymptotic, and explicit error bounds for the accuracy of the selected roots in terms of fundamental model parameters. All results hold under a natural separation condition on the correct signal frequencies and are applicable to several versions of the problem which are used in practice.
September 11
(CUNY closed, no seminar)
September 18
Speaker: Junren Chen (Columbia University)
Title:
Abstract:
September 25
Speaker: Alan Chang (Washington University, St. Louis)