UBC Mathematics Department
http://www.math.ubc.ca
Abstract: The spectral estimation of stationary time series is well developed and plays an important role in many applications such as seismology, economics, meteorology, etc. But physical processes are never stationary; there are always slow variations and trends that make the existing theory difficult to apply in a systematic way, without expert human intervention. Using the technology of the adaptive local cosine transform we show how to estimate (compress) locally stationary signals in a very efficient way. We will also discuss possible extensions to piecewise locally stationary processes that arise in many applications, in seismology for example.
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