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.
E-mail: pdbaxt@maths.leeds.ac.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.