Mathematical modelling of a first order sigma-delta modulator

Abstract

In this paper an exact model for a basic, first order sigma-delta modulator is derived by means of a difference equation with discontinuous nonlinearity. An explicit solution is given in terms of the greatest integer function under certain boundedness and initial conditions of the input signal. Assumptions are made under which the explicit formula remains a solution of the difference equation although the suppositions of the main theorem are violated.

Keywords:

• Discontinuous difference equations
• Sigma-Delta modulator
• Exact solution
• Greatest integer function

AMS Subject Classfication:

• 94A14
• 39A10
• 11B34