Signal representation by adaptive biased wavelet expansions

This paper reviews a technique of adaptive wavelet expansions and introduces the novel concept of "biased wavelets." These are functions that are localized in time and in frequency but, unlike conventional wavelets, have an adjustable nonzero mean component. Under mild conditions, it is shown that a conventional mother wavelet can be used to construct a family of biased wavelets which spans the set of finite-energy functions L-2(R). Numerical tests suggest that the introduction of the adjustable "bias" considerably improves the representation capabilities of wavelet expansions. A problem of electrocardiographic data compression is used for illustration purposes. Test signals were extracted from the MIT-BIH ECG Compression Test Database. (C)1999 Academic Press.