Decimation filters for oversampled analog to digital converters based on quadratic programming

A description is given of a quadratic-programming-based methodology for the design of decimation filters in CMOS technology. The methodology presented tackles the filter design problem by formulating a quadratic programming problem that minimizes the integral of the aliased noise subject to the passband and stopband constraints. This methodology offers the flexibility of incorporating nonsinusoidal quantization noise spectral density in the design process. Moreover the filter response can be optimized to meet arbitrary antialias requirements. Because the projected hessian matrix of the objective function is positive definite, the quadratic function has a unique minimum