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.

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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

Tags

DTIC Thesaurus Topics

  • Analyzers
  • Bandwidth
  • Contracts
  • Demodulation
  • Engineering
  • Equations
  • Experimental Data
  • Fourier Analysis
  • Frequency Bands
  • Frequency Response
  • Identities
  • Maximum Likelihood Estimation
  • Military Research
  • Power Spectra
  • Random Variables
  • Spectrum Analyzers
  • Statistics

Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Linear Algebra
  • Spectroscopy.