Linear Prediction of Discrete-Time 1/f Processes
Journal article, 2010

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.

fractional Gaussian noise




spectral flatness measure

Fractional Brownian motion

image texture


fractional brownian-motion


S. Yousefi

Royal Institute of Technology (KTH)

J. Jalden

Royal Institute of Technology (KTH)

Thomas Eriksson

Chalmers, Signals and Systems, Communication and Antenna Systems, Communication Systems

IEEE Signal Processing Letters

1070-9908 (ISSN)

Vol. 17 11 901-904

Subject Categories

Computer and Information Science



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