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Differentiating noisy radiocommunications signals: wavelet estimation of a derivative in the presence of heteroscedastic noise


Paul D. Baxter, Department of Statistics, University of Leeds, Leeds, LS2 9JT, UK.


Summary.  Radio scientists require estimates of the rate of change in rain-induced signals. Unfortunately, these signals are observed in the presence of atmospheric noise, which has a variance that is dependent on temperature, pressure and other climatic variables. We develop a systematic approach to the problem, using wavelet differentiation combined with coefficient-dependent thresholding, and illustrate the considerable benefits that this provides over more conventional techniques.