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Recursive maximum likelihood estimation of complex autoregressive processes

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Abstract

The recursive maximum likelihood estimation (RMLE) algorithm conceived by Kay (see ibid., vol.ASSP-31, p.56, 1983) is extended to complex data sets. The complex version requires the same level of computation as that for real data. The original development was restricted to the case of realm data. The purpose is to extend RMLE to the more universal realm of complex data. The derivation is discussed. It is argued, without direct proof, that the algorithm is stable in the sense that the magnitude of the reflection coefficient at each step is less than unity

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  • C Chamzasio
  • A T Walden
A. Papoulis and C. Chamzas, " Detection of hidden periodicities by adaptive extrapolation, " IEEE Trans. Acoust., Speech, Signal Pro-cessing, vol. ASSP-27, no. 5, pp. 492-500, Oct. 1979. [IO] A. T. Walden, " Non-Gaussian reflectivity, entropy, and deconvolu-tion, " Geophysics, vol. 50, no. 12, pp. 2862-2888, Dec. 1985. [ I I] M. I. Sezan and A. M. Tekalp, " Iterative image restoration with ring-ing suppression using the method of POCS, " in Proc. IEEE Int. Conf. Acoust., Speech, Signal Processing (New York, NY), Apr. 1988, pp. 1300-1303. 871-874.
Deconvolution with the I , norm
  • H L Taylor
  • S C Banks
  • J F Mccoy
I] H. L. Taylor, S. C. Banks, and J. F. McCoy, " Deconvolution with the I, norm, " Geophysics, vol. 44, no. 1, pp. 39-52, Jan. 1979.
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  • R Yargaladda
  • J B Bedmar
  • T L Watt
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