Time-Angle Periodically Correlated Processes

  • Jérôme AntoniEmail author
  • Dany Abboud
  • Sophie Baudin
Part of the Lecture Notes in Mechanical Engineering book series (LNME)


Cyclostationary processes have now become an essential mathematical representation of vibration and acoustical signals produced by rotating machines. However, to be applicable the approach requires the rotational speed of the machine to be constant, which imposes a limit to several applications. The object of this chapter is to introduce a new class of processes, coined time-angle periodically correlated, which extends second-order cyclostationary processes to varying regimes. Such processes are fully characterized by a time-angle autocorrelation function and its double Fourier transform, the frequency-order spectral correlation. The estimation of the latter quantity is briefly discussed and demonstrated on a real-world vibration signal captured during a run-up.


Cyclostationary processes Periodically correlated processes Spectral correlation Non-stationary regime Vibration signals Acoustics 


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Laboratoire Vibrations Acoustique (LVA)University of LyonVilleurbanneFrance
  2. 2.Centre Technique des Industries Mécaniques (CETIM)SenlisFrance
  3. 3.Laboratoire de Mecanique des Contacts et des Structures (LaMCoS) UMR5259University of LyonVilleurbanneFrance

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