Cramer-Rao Bound Analysis for Frequency Estimation of Sinusoids in Noise

Abstract

The Cramer-Rao inequality is used to determine a lower bound on the variance with which a sinusoidal frequency can be estimated in the presence of Gaussian white noise. A parametric study has elucidated the influence of number of samples (N), sampling frequency (1/delta), phase (phi), and signal-to-noise ratio on the Cramer-Rao bound. A closed form expression for the asymptotic level to which the Cramer-Rao bound decays is characterized and, for low frequencies, the bound is determined analytically and graphically. The form of the Cramer-Rao bound is linked to resolution in the sampling problem. Identification of trade- offs characterizing the sensitivity of the bound and parameters associated with it are discussed.

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Document Details

Document Type
Technical Report
Publication Date
Mar 24, 1986
Accession Number
ADA167992

Entities

People

  • Joy M. Skon

Organizations

  • Massachusetts Institute of Technology

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Abstracts
  • Air Force
  • Contracts
  • Equations
  • Frequency
  • Intervals
  • Massachusetts
  • Measurement
  • Noise
  • Numbers
  • Sampling
  • Sine Waves
  • Square Waves
  • United States
  • United States Government
  • Waves
  • White Noise

Fields of Study

  • Engineering

Readers

  • Radar Systems Engineering.
  • Statistical inference.