Abstract
We seek optimal methods of estimating power spectrum and chirp (frequency change) rate for the case that one has incomplete noisy data on values y(t) of a time series. The Schuster periodogram turns out to be a “sufficient statistic” for the spectrum, a generalization playing the same role for chirped signals. However, the optimal processing is not a linear filtering operation like the Blackman-Tukey smoothing of the periodogram, but rather a nonlinear operation. While suppressing noise/side lobe artifacts, it achieves the same kind of improved resolution that the Burg method did for noiseless data.
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Jaynes, E.T. (1987). Bayesian Spectrum and Chirp Analysis. In: Smith, C.R., Erickson, G.J. (eds) Maximum-Entropy and Bayesian Spectral Analysis and Estimation Problems. Fundamental Theories of Physics, vol 21. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-3961-5_1
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DOI: https://doi.org/10.1007/978-94-009-3961-5_1
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