On the Design of Optimal Noise Transfer Functions for Delta–Sigma Modulators

One of the popular methods of designing a noise transfer function (NTF) used in the synthesis of a delta-sigma modulator (DSM) is to optimally place its zeros across the signal band of interest while minimizing the in-band noise power. The distribution of the poles of the NTF is considered secondary. In this brief, we provide a method to design a discrete-time NTF from a normalized analog highpass filter in which the coefficients of the characteristic polynomial of the squared-magnitude function of the filter are optimized to minimize the energy in the band of interest, in addition to satisfying the realizability constraints required to synthesize a DSM. We compare the performance of the NTFs designed using our method with those designed using one of the well-known methods in terms of the signal-to-quantization noise ratio (SQNR). It is shown that the SQNR of the NTFs designed using our method is higher than that of the NTFs designed using the well-known methods.