Linear Prediction of Discrete-Time 1/f Processes
2010 (English)In: IEEE Signal Processing Letters, ISSN 1070-9908, E-ISSN 1558-2361, Vol. 17, no 11, 901-904 p.Article in journal (Refereed) Published
In this letter, the linear predictability of discrete-time stationary stochastic processes with 1/vertical bar f vertical bar(alpha)-shaped power spectral density (PSD) is considered. In particular, the spectral flatness measure (SFM)-which yields a lower bound for the normalized mean-squared-error (NMSE) of any linear one-step-ahead (OSA) predictor-is obtained analytically as a function of alpha is an element of [0, 1]. By comparing the SFM bound to the NMSE of the p-tap linear minimum-mean-square error (LMMSE) predictor, it is shown that close to optimal NMSE performance may be achieved for relatively moderate values of. The performance of the LMMSE predictor for the discrete-time fractional Gaussian noise (DFGN), which may be viewed as the conventional discrete-time counterpart of continuous-time processes with 1/vertical bar f vertical bar(alpha)-shaped PSD, shows that the DFGN is more easily predicted than the discrete-time processes considered herein.
Place, publisher, year, edition, pages
2010. Vol. 17, no 11, 901-904 p.
Fractional Brownian motion, fractional Gaussian noise, linear prediction, spectral flatness measure, 1/f-process
IdentifiersURN: urn:nbn:se:kth:diva-26274DOI: 10.1109/LSP.2010.2070064ISI: 000283243200001ScopusID: 2-s2.0-77956407180OAI: oai:DiVA.org:kth-26274DiVA: diva2:387541
QC 201101142011-01-142010-11-212011-01-14Bibliographically approved