Introduction to numerical analysis: 2nd edition
Introduction to numerical analysis: 2nd edition
Multirate systems and filter banks
Multirate systems and filter banks
Discrete-time signal processing (2nd ed.)
Discrete-time signal processing (2nd ed.)
A sampling expansion for nonbandlimited signals in chromatic derivatives
IEEE Transactions on Signal Processing
Generalizations of chromatic derivatives and series expansions
IEEE Transactions on Signal Processing
Signal interpolation using numerically robust differential operators
ICS'10 Proceedings of the 14th WSEAS international conference on Systems: part of the 14th WSEAS CSCC multiconference - Volume II
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We present a detailed motivation for the notions of chromatic derivatives and chromatic expansions. Chromatic derivatives are special, numerically robust linear differential operators; chromatic expansions are the associated local expansions, which possess the best features of both the Taylor and the Nyquist expansions. We give a simplified treatment of some of the basic properties of chromatic derivatives and chromatic expansions which are relevant for applications. We also consider some signal spaces with a scalar product defined by a Cesàro-type sum of products of chromatic derivatives, as well as an approximation of such a scalar product which is relevant for signal processing. We also introduce a new kind of local approximations based on trigonometric functions.