Cramer-Rao Bound Analysis for Frequency Estimation of Sinusoids in Noise
MASSACHUSETTS INST OF TECH LEXINGTON LINCOLN LAB
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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 1delta, 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.
- Statistics and Probability