Cramer-Rao bound and optimal amplitude estimator of superimposed sinusoidal signals with unknown frequencies

Author

Shaohui Jia, Louisiana Tech University

Date of Award

Spring 2000

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Computational Analysis and Modeling

First Advisor

Albert Alexander

Abstract

This dissertation addresses optimally estimating the amplitudes of superimposed sinusoidal signals with unknown frequencies. The Cramer-Rao Bound of estimating the amplitudes in white Gaussian noise is given, and the maximum likelihood estimator of the amplitudes in this case is shown to be asymptotically efficient at high signal to noise ratio but finite sample size. Applying the theoretical results to signal resolutions, it is shown that the optimal resolution of multiple signals using a finite sample is given by the maximum likelihood estimator of the amplitudes of signals.

Recommended Citation

Jia, Shaohui, "" (2000). Dissertation. 182.
https://digitalcommons.latech.edu/dissertations/182