Quadratic Estimators of the Power Spectrum
Abstract
Among nonparametric estimators of the power spectrum, quadratic estimators are the only ones that are dimensionally correct. This report motivates interest in quadratic estimators by setting up idealized experiments for spectrum analysis and deriving maximum likelihood estimates for narrowband power. These idealized experiments show that quadratic functions of the experimental data are sufficient statistics for estimating power. The maximum likelihood estimates show that low-rank projection operators play a fundamental role in the theory of spectrum analysis. The projection operator plays the same role as a bandpass filter in a conventional swept frequency spectrum analyzer. The mean-squared error of a maximum likelihood estimator of power is inversely proportional to the rank of the estimator. With our maximum likelihood result in hand, we turn to a systematic study of quadratic estimators of the power spectrum. Keywords: Heuristic methods, Covariance.
Document Details
- Document Type
- Technical Report
- Publication Date
- Apr 01, 1989
- Accession Number
- ADA208601
Entities
People
- C. T. Mullis
- Louis L. Scharf
Organizations
- University of Colorado Boulder