TY - JOUR

T1 - Optimal fractional linear prediction with restricted memory

AU - Skovranek, Tomas

AU - Despotovic, Vladimir

AU - Peric, Zoran

N1 - Funding Information:
Manuscript received February 15, 2019; accepted March 22, 2019. Date of publication March 29, 2019; date of current version April 10, 2019. This work was supported in part by the Slovak Research and Development Agency under Grants SK-SRB-18-0011, SK-AT-2017-0015, and APVV-14-0892; in part by the Slovak Grant Agency for Science under Grant VEGA 1/0365/19; in part by the Ministry of Education, Science and Technological Development of the Republic of Serbia under Grants 337-00-107/2019-09/11 and TR33037; and in part by the framework of the COST Action CA15225. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Rosangela Fernandes Coelho. (Corresponding author: Tomas Skovranek.) T. Skovranek is with the BERG Faculty, Technical University of Kosice, Kosice 04200, Slovakia (e-mail:,tomas.skovranek@tuke.sk).
Publisher Copyright:
© 1994-2012 IEEE.

PY - 2019/5

Y1 - 2019/5

N2 - Linear prediction is extensively used in modeling, compression, coding, and generation of speech signal. Various formulations of linear prediction are available, both in time and frequency domain, which start from different assumptions but result in the same solution. In this letter, we propose a novel, generalized formulation of the optimal low-order linear prediction using the fractional (non-integer) derivatives. The proposed fractional derivative formulation allows for the definition of predictor with versatile behavior based on the order of fractional derivative. We derive the closed-form expressions of the optimal fractional linear predictor with restricted memory, and prove that the optimal first-order and the optimal second-order linear predictors are only its special cases. Furthermore, we empirically prove that the optimal order of fractional derivative can be approximated by the inverse of the predictor memory, and thus, it is a priori known. Therefore, the complexity is reduced by optimizing and transferring only one predictor coefficient, i.e., one parameter less in comparison to the second-order linear predictor, at the same level of performance.

AB - Linear prediction is extensively used in modeling, compression, coding, and generation of speech signal. Various formulations of linear prediction are available, both in time and frequency domain, which start from different assumptions but result in the same solution. In this letter, we propose a novel, generalized formulation of the optimal low-order linear prediction using the fractional (non-integer) derivatives. The proposed fractional derivative formulation allows for the definition of predictor with versatile behavior based on the order of fractional derivative. We derive the closed-form expressions of the optimal fractional linear predictor with restricted memory, and prove that the optimal first-order and the optimal second-order linear predictors are only its special cases. Furthermore, we empirically prove that the optimal order of fractional derivative can be approximated by the inverse of the predictor memory, and thus, it is a priori known. Therefore, the complexity is reduced by optimizing and transferring only one predictor coefficient, i.e., one parameter less in comparison to the second-order linear predictor, at the same level of performance.

KW - Fractional calculus

KW - linear prediction

KW - restricted memory

KW - speech processing

UR - http://www.scopus.com/inward/record.url?scp=85064602198&partnerID=8YFLogxK

U2 - 10.1109/LSP.2019.2908278

DO - 10.1109/LSP.2019.2908278

M3 - Article

AN - SCOPUS:85064602198

VL - 26

SP - 760

EP - 764

JO - IEEE Signal Processing Letters

JF - IEEE Signal Processing Letters

SN - 1070-9908

IS - 5

M1 - 8676355

ER -