Statistical analysis of Capon-Bartlett 2-D cross spectrum
An exact joint probability density function (PDF) (not approximate as in [4]) is provided for the Capon power spectral estimate and the average output power of any other deterministic filter when based on the same data sample covariance matrix. The cross coherence/cosine (correlation coefficient) between the two filter weights determines the extent of statistical dependence. An exact PDF for a sample covariance based (SCB) estimate of this cross coherence is derived allowing complete point-level statistical characterization of the 2-D Capon-Bartlett cross spectrum introduced in [4]. The exact bias and variance are computed for the cross spectrum showing asymptotic consistency and inviting a natural recursive refinement for reducing bias. ©2010 IEEE.
