CramerRao bound analysis for frequency estimation of sinusoids in noise
Abstract
The CramerRao 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 CramerRao bound. A closed form expression for the asymptotic level to which the CramerRao bound decays is characterized and, for low frequencies, the bound is determined analytically and graphically. The form of the CramerRao bound is linked to resolution in the sampling problem. Identification of tradeoffs characterizing the sensitivity of the bound and parameters associated with it are discussed.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 March 1986
 Bibcode:
 1986STIN...8710227S
 Keywords:

 Analysis Of Variance;
 Frequency Distribution;
 Inequalities;
 Maximum Likelihood Estimates;
 Oscillations;
 Random Noise;
 Signal To Noise Ratios;
 Sine Waves;
 White Noise;
 Asymptotic Methods;
 Linkages;
 Low Frequencies;
 Matrices (Mathematics);
 Sampling;
 Tradeoffs;
 Communications and Radar