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SUMMARY:Methods for the Periodically Correlated Random Processes: Estimati
 on\, Decomposition\, Modelling - Ihor Isayev\, Karpenko Physico-mechanical
  Institute of NAS of Ukraine
DTSTART:20070608T143000Z
DTEND:20070608T160000Z
UID:TALK7520@talks.cam.ac.uk
CONTACT:Taylan Cemgil
DESCRIPTION:Periodically correlated random processes (PCRP\, also known as
  Cyclostationary or periodically non-stationary) is an adequate model for 
 describing the physical phenomena\, where stochasticity and recurrence pla
 y significant role. The PCRP properties\, in Gaussian assumption\, can be 
 described by first- and second-order probabilistic characteristics – the
  mean\, correlation function and spectral density. Estimating operators fo
 r these characteristics (as well as for any other kind of non-stationarity
 ) should be deduced taking into account their time variability\, finite re
 cord length\, and possibility to estimate the signal characteristics for u
 nit record (so called ergodicity problem). The coherent method\, which is 
 based on averaging the signal values via correlation period\, and the comp
 onent method\, which is based on the Fourier transform will be shown. Comp
 arision between the coherent and component estimates will be carried out. 
 Also\, I focus attention on the methods for hidden periodicity search.\nAn
  important part for understanding the PCRP structure is the PCRP decomposi
 tion into stationary connected random processes (harmonic serial represent
 ation). Provided the specific form for the harmonic components\, we can co
 nstruct the additive\, multiplicative\, poly-harmonic models\, etc. Based 
 on this\, we develop the new algorithm for PCRP decomposition and the new 
 approach for PCRP parametrical modelling.\nThe practical usage of PCRP met
 hods will be shown for vibro-acoustic and music examples.\n
LOCATION:Engineering Department\, Baker Building\, Division F meeting room
 \, 5th floor
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