In this chapter an abstract model of a noise-shaping quantizer is derived. A noise-shaping quantizer is a more general description of a sigma-delta modulator, consisting of one or more cost functions and a selection function. The cost function is an indication of the quality of a signal or an encoding solution, and the selection function determines the output symbol. In the case of a normal sigma-delta modulator the cost function is implemented by the loop-filter and the selection function by the quantizer. This generalization of the sigma-delta modulator structure will enable to addition of look-ahead functionality in the next chapter.