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Linear Prediction of Discrete-Time 1/f Processes
KTH, School of Electrical Engineering (EES), Signal Processing.
KTH, School of Electrical Engineering (EES), Signal Processing.ORCID iD: 0000-0001-6630-243X
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
Abstract [en]

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.
Keyword [en]
Fractional Brownian motion, fractional Gaussian noise, linear prediction, spectral flatness measure, 1/f-process
National Category
Signal Processing
Identifiers
URN: urn:nbn:se:kth:diva-26274DOI: 10.1109/LSP.2010.2070064ISI: 000283243200001Scopus ID: 2-s2.0-77956407180OAI: oai:DiVA.org:kth-26274DiVA: diva2:387541
Note
QC 20110114Available from: 2011-01-14 Created: 2010-11-21 Last updated: 2017-12-11Bibliographically approved

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Jalden, Joakim

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