The fast growth of the applied area of analog-to-digital conversion has simultaneously hindered the solid establishment of its mathematical foundations. This has become particularly critical with the currently successful technique of modulation, as recent results of the principal investigator have shown the inaccuracy of the conversion error model universally adopted until now. The research proposed in this project is based on recent discoveries of fundamental algebraic properties of n th order modulators and aims at establishing the first general algebraic foundations to modulation. On going research has already proved effective in correcting the classical error model. Although new practical improved techniques may not be the immediate outcome to this small grant proposal, the establishments of solid foundations will enable the growth of powerful analytical tools, opening new directions of design not accessible by the currently empirical approach to modulation.
