TY - JOUR

T1 - Memory-m antipodal processes: Spectral analysis and synthesis

AU - Rovatti, Riccardo

AU - Mazzini, Gianluca

AU - Setti, Gianluca

N1 - Generated from Scopus record by KAUST IRTS on 2023-02-15

PY - 2009/1/1

Y1 - 2009/1/1

N2 - Discrete-time two-valued processes are of paramount importance in Information Engineering and their analysis is usually addressed assuming they have at most the memory of one step in the past. Since this is a quite limiting assumption, a general analytic formula is given here for the spectrum of stochastic antipodal processes with finite memory-m ≤ 1. [The formula is derived within a generalized Markov framework and depends on the eigenstructure of a suitably defined transition matrix that is also exploited to give ergodicity conditions. The complexity of the overall analysis depends on the size of such matrix which is exponential in. [Within that framework a slightly less general but more tractable scheme for the generation of antipodal processes with prescribed spectral profile is introduced leveraging on a linear probability feedback. For such a scheme, whose complexity is linear in, an alternative spectrum formula is derived as well as a synthesis procedure going from spectrum specification to feedback filter design. Both the general case and the linear probability feedback scheme are exemplified in some special cases. © 2009 IEEE.

AB - Discrete-time two-valued processes are of paramount importance in Information Engineering and their analysis is usually addressed assuming they have at most the memory of one step in the past. Since this is a quite limiting assumption, a general analytic formula is given here for the spectrum of stochastic antipodal processes with finite memory-m ≤ 1. [The formula is derived within a generalized Markov framework and depends on the eigenstructure of a suitably defined transition matrix that is also exploited to give ergodicity conditions. The complexity of the overall analysis depends on the size of such matrix which is exponential in. [Within that framework a slightly less general but more tractable scheme for the generation of antipodal processes with prescribed spectral profile is introduced leveraging on a linear probability feedback. For such a scheme, whose complexity is linear in, an alternative spectrum formula is derived as well as a synthesis procedure going from spectrum specification to feedback filter design. Both the general case and the linear probability feedback scheme are exemplified in some special cases. © 2009 IEEE.

UR - https://ieeexplore.ieee.org/document/4472849

UR - http://www.scopus.com/inward/record.url?scp=60649093516&partnerID=8YFLogxK

U2 - 10.1109/TCSI.2008.920986

DO - 10.1109/TCSI.2008.920986

M3 - Article

SN - 1057-7122

VL - 56

SP - 156

EP - 167

JO - IEEE Transactions on Circuits and Systems I: Regular Papers

JF - IEEE Transactions on Circuits and Systems I: Regular Papers

IS - 1

ER -