In this paper a framework for the analysis of a family of high order interpolative sigma-delta modulators is introduced. It is shown that a large number of high order architectures can be reduced to a diagonal form which facilitates the stability analysis of the system. In addition, the diagonal form is a canonical form which illustrates the equivalence of a variety of sigma-delta architectures. Architectural di erences are manifested as di erences in parameter values in the diagonal form, providing a convenient method of comparison between systems. It is also shown how transformation to the diagonal form may result in a reduction in order of a system. Finally, there is a brief discussion on the importance of diagonal systems as opposed to non-diagonal systems.
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