##
TR#556:

## Bayesian Spectrum Estimation of Unevenly Sampled Nonstationary
Data

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Yuan Qi, Thomas P. Minka, and Rosalind W. Picard

September, 2002

Spectral estimation methods typically assume stationarity and uniform
spacing between samples of data. The non-stationarity of real data is
usually accommodated by windowing methods, while the lack of
uniformly-spaced samples is typically addressed by methods that ``fill
in'' the data in some way. This paper presents a new approach to both
of these problems: we use a Bayesian framework, which includes a
non-stationary Kalman filter, to jointly estimate all spectral
coefficients instantaneously.
The new method works regardless whether the samples are evenly or
unevenly spaced; moreover, it provides a new approach to enabling
processing when it is desirable to virtually eliminate aliasing by
unevenly sampling. An
amplitude-preservation property of the new method can be used to
detect if aliasing occurred.
Finally, we propose an efficient algorithm for sparsifying the
spectrum estimates when we know a priori that the signal is
narrow-band in the frequency domain. We illustrate the new method on
several data sets, showing that it can perform well on unevenly
sampled nonstationary signals without the use of any sliding window,
that it can estimate frequency components beyond half of the
average sampling frequency when the signal is unevenly sampled, and
that it can provide more accurate estimation than several other important
recent and classical methods.

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