Local stationarity of L2(ℝ) processes

@article{Garcia2002LocalSO,
  title={Local stationarity of L2(ℝ) processes},
  author={Francisco M. Garcia and I.M.G. Lourtie and J. Buescu},
  journal={2002 IEEE International Conference on Acoustics, Speech, and Signal Processing},
  year={2002},
  volume={2},
  pages={II-1221-II-1224}
}
  • Francisco M. Garcia, I.M.G. Lourtie, J. Buescu
  • Published 2002
  • Mathematics, Computer Science
  • 2002 IEEE International Conference on Acoustics, Speech, and Signal Processing
  • This paper shows how the sampling theorem relates with the variations along time of the second order statistics of L2(ℝ) nonstationary processes. As a consequence, and mainly due to the positive semidefiniteness of autocorrelation functions, it is possible to conclude if a nonstationary process is locally stationary (i.e., if its second order statistics vary slowly along time) by the direct observation of its 2-dimension power spectrum or its Wigner distribution. A simple example illustrates… CONTINUE READING
    2 Citations
    Estimation of locally stationary covariance matrices from data
    • F. Garcia, I. Lourtie
    • Computer Science, Mathematics
    • 2003 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003. Proceedings. (ICASSP '03).
    • 2003
    • 1
    • Highly Influenced
    Detection of transient signals with unknown localization
    • 2

    References

    SHOWING 1-10 OF 14 REFERENCES
    L/sup 2/(R) nonstationary processes and the sampling theorem
    • 15
    Wigner-Ville spectral analysis of nonstationary processes
    • 563
    • PDF
    Efficiency of real-time Gaussian transient detectors: comparing the Karhunen-Loeve and the wavelet decompositions
    • F. Garcia, I. Lourtie
    • Computer Science
    • 2000 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.00CH37100)
    • 2000
    • 4
    A sampling theorem for nonstationary random processes (Corresp.)
    • W. Gardner
    • Mathematics, Computer Science
    • IEEE Trans. Inf. Theory
    • 1972
    • 33
    Stochastic Processes in Engineering Systems
    • 339
    and Z
    • Zhang, “Adaptive covariance estimation of locally stationary processes,” Ann. Statist., vol. 26
    • 1998
    Lourtie, “Positivedefiniteness, integral equations and Fourier transforms,
    • Departamento de Matemática, IST
    • 2000
    L2(li) non­ stationary processes and the sampling theorem
    • IEEE Signal Processing Letters
    • 2001