Noise Weighting in the Design of $\Delta \Sigma$ Modulators (With a Psychoacoustic Coder as an Example)

A design flow for ΔΣ modulators is illustrated, allowing quantization noise to be shaped according to an arbitrary weighting profile. Based on finite-impulse-response noise transfer functions, possibly with high order, the flow is best suited for digital architectures. This work builds on a recent proposal in which the modulator is matched to the reconstruction filter, showing that this type of optimization can benefit a wide range of applications in which noise (including in-band noise) is known to have a different impact at different frequencies. The designs of a multiband modulator, a modulator avoiding dc noise, and an audio modulator capable of distributing quantization artifacts according to a psychoacoustic model are discussed as examples. A software toolbox is provided as a general design aid and to replicate the proposed results.