Kullback-Leibler approximation of spectral density functions

@article{Georgiou2003KullbackLeiblerAO,
  title={Kullback-Leibler approximation of spectral density functions},
  author={Tryphon T. Georgiou and Anders Lindquist},
  journal={IEEE Trans. Information Theory},
  year={2003},
  volume={49},
  pages={2910-2917}
}
We introduce a Kullback–Leibler-type distance between spectral density functions of stationary stochastic processes and solve the problem of optimal approximation of a given spectral density by one that is consistent with prescribed second-order statistics. In general, such statistics are expressed as the state covariance of a linear filter driven by a stochastic process whose spectral density is sought. In this context, we show i) that there is a unique spectral density which minimizes this… CONTINUE READING
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