Hardware reduction in digital delta-sigma modulators via error masking - part II: SQ-DDSM

In this two-part paper, a design methodology for reduced-complexity digital delta-sigma modulators (DDSMs) based on error masking is presented. Rules for selecting the wordlengths of the stages in multistage architectures are elaborated. We show that the hardware requirement can be reduced by up to 20% compared with a conventional design, without sacrificing performance. Simulation results confirm theoretical predictions. Part I addresses multistage noise-shaping DDSMs, whereas Part II focuses on single-quantizer DDSMs

Hardware reduction in digital delta-sigma modulators via error masking - part I: MASH DDSM

Two classes of techniques have been developed to whiten the quantization noise in digital delta-sigma modulators (DDSMs): deterministic and stochastic. In this two-part paper, a design methodology for reduced-complexity DDSMs is presented. The design methodology is based on error masking. Rules for selecting the word lengths of the stages in multistage architectures are presented. We show that the hardware requirement can be reduced by up to 20% compared with a conventional design, without sacrificing performance. Simulation and experimental results confirm theoretical predictions. Part I addresses MultistAge noise SHaping (MASH) DDSMs; Part II focuses on single-quantizer DDSMs.

Reduced complexity MASH delta-sigma modulator

A reduced complexity digital multi-stage noise shaping (MASH) delta-sigma modulator for fractional-N frequency synthesizer applications is proposed. A long word is used for the first modulator in a MASH structure; the sequence length is maximized by setting the least significant bit of the input to 1; shorter words are used in subsequent stages. Experimental results confirm simulation

Solving Inverse Problems with Reinforcement Learning

In this paper, we formally introduce, with rigorous derivations, the use of reinforcement learning to the field of inverse problems by designing an iterative algorithm, called REINFORCE-IP, for solving a general type of non-linear inverse problem. By choosing specific probability models for the action-selection rule, we connect our approach to the conventional regularization methods of Tikhonov regularization and iterative regularization. For the numerical implementation of our approach, we parameterize the solution-searching rule with the help of neural networks and iteratively improve the parameter using a reinforcement-learning algorithm~-- REINFORCE. Under standard assumptions we prove the almost sure convergence of the parameter to a locally optimal value. Our work provides two typical examples (non-linear integral equations and parameter-identification problems in partial differential equations) of how reinforcement learning can be applied in solving non-linear inverse problems. Our numerical experiments show that REINFORCE-IP is an efficient algorithm that can escape from local minimums and identify multi-solutions for inverse problems with non-uniqueness.Comment: 33 pages, 10 figure