We present an intrinsic metric that quantifies distances between power spectral density functions. The metric was derived by Georgiou as the geodesic distance between spectral density functions with respect to a particular pseudo-Riemannian metric motivated by a quadratic prediction problem. We provide an independent verification of the metric inequality and discuss certain key properties of the induced topology.
Bibliographical noteFunding Information:
Manuscript received August 19, 2006; revised November 10, 2006. This work was supported by the National Science Foundation, the Air Force Office of Scientific Research, and the Vincentinne Hemes–Luh Chair. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Deniz Erdogmus.
- Information geometry
- Intrinsic metric
- Power spectral density functions