Distances between power spectral densities
| dc.creator | Georgiou, Tryphon T. | |
| dc.date | 2006-07-01 | |
| dc.date | 2006-07-29 | |
| dc.date.accessioned | 2026-07-07T09:51:09Z | |
| dc.date.available | 2026-07-07T09:51:09Z | |
| dc.description | We present several natural notions of distance between spectral density functions of (discrete-time) random processes. They are motivated by certain filtering problems. First we quantify the degradation of performance of a predictor which is designed for a particular spectral density function and then it is used to predict the values of a random process having a different spectral density. The logarithm of the ratio between the variance of the error, over the corresponding minimal (optimal) variance, produces a measure of distance between the two power spectra with several desirable properties. Analogous quantities based on smoothing problems produce alternative distances and suggest a class of measures based on fractions of generalized means of ratios of power spectral densities. These distance measures endow the manifold of spectral density functions with a (pseudo) Riemannian metric. We pursue one of the possible options for a distance measure, characterize the relevant geodesics, and compute corresponding distances. | |
| dc.description | 16 pages, 4 figures; revision (July 29, 2006) includes two added sections | |
| dc.identifier | https://arxiv.org/abs/math/0607026 | |
| dc.identifier | http://arxiv.org/abs/math/0607026 | |
| dc.identifier | IEEE Transactions on Signal Processing, vol. 55(8), pages 3995-4003, August 2007. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/165188 | |
| dc.subject | Optimization and Control | |
| dc.subject | 60G10 | |
| dc.title | Distances between power spectral densities | |
| dc.type | text |