A control-bounded analog-to-digital converter consists of a linear analog system that is subject to digital control, and a digital filter that estimates the analog input signal from the digital control signals. Such converters have many commonalities with delta–sigma converters, but they can use more general analog filters. The paper describes the operating principle, gives a transfer function analysis, and describes the digital filtering. In addition, the paper discusses two examples of such architectures. The first example is a cascade structure reminiscent of, but simpler than, a high-order MASH converter. The second example combines two attractive properties that have so far been considered incompatible. Its nominal conversion noise (assuming ideal components) essentially equals that of the first example. However, its analog filter is a fully connected network to which the input signal is fed in parallel, which potentially makes it more robust against nonidealities.

This article presents analytical tools for high-level design of the leapfrog (LF) control-bounded analog-to-digital converter (CBADC). We derive closed-form design equations for parameterizing the analog system for a target signal-to-noise ratio (SNR) and bandwidth. Furthermore, we show how the parameterization can be modified to compensate for finite amplifier gain-bandwidth product (GBWP) and to control the signal swing at different nodes of the system. Behavioral circuit simulations are used to compare the LF CBADC to relevant continuous-time sigma–delta modulators (CT- $\Sigma \Delta $ Ms) in terms of nominal performance and sensitivity to component variations, clock jitter, and finite GBWP. Simulations show that the nominal performance of the LF is similar to that of a CT- $\Sigma \Delta \text{M}$ of the same loop-filter order and with the same number of quantization levels. The simple, modular structure, analytical stability guarantee, and single-bit quantizers make the LF an interesting alternative to conventional CT- $\Sigma \Delta $ Ms.

In this paper, behavioural circuit simulations are used to compare the leapfrog control-bounded analog-to-digital converter to relevant continuous-time sigma-delta modulators in terms of nominal performance and sensitivity to component variations, clock jitter and finite gain-bandwidth product. Simulations show that the nominal performance of the leapfrog is similar to that of a continuous-time sigma-delta modulator of the same loop filter order and with the same number of quantization levels. Component variations in the leapfrog's analog system will introduce errors in the final output, unless the coefficients of the reconstruction filter are modified accordingly. Nevertheless, the simple, modular structure, analytical stability guarantee and single-bit quantizers make the leapfrog an interesting alternative to conventional continuous-time sigma-delta modulators.

The paper considers the problem of joint system identification and input signal estimation of an unknown linear system from noisy observations of the output signal. The input signal is assumed to be sparse, and each individual input pulse may affect the system in its own (and unknown) way. Based on ideas from sparse Bayesian learning, we derive an efficient expectation maximization (EM) algorithm for jointly estimating all unknown quantities. Unlike related prior work, the proposed algorithm does not alternate between estimating the input signal and estimating the system parameters; instead, all unknown quantities are jointly updated in each EM step. We give closed-form expressions for these EM updates, which can be efficiently computed by Gaussian message passing.

The rapid progress of invasive therapeutic options for cardiac arrhythmias increases the need for accurate diagnostics. The surface electrocardiogram (ECG) is still the standard of noninvasive diagnostics but lacks atrial signal resolution. By contrast, esophageal electrocardiography (EECG) yields atrial signals of high amplitude and with a high signal-to-noise ratio. Esophageal electrocardiography has become fast and safe, but the mechanical constraints of esophageal measuring catheters and the “random” motion of the catheter inside the subject’s esophagus limit the spatial resolution of EECG signals. In this paper, we propose a method to estimate the electrical field projected onto the esophagus with an increased spatial resolution, using commonly available esophageal catheters. In a first step, we estimate the time-varying catheter position, and in a second step, we estimate the projected electrical field with enhanced spatial resolution. The proposed algorithm comprises several consecutive optimization steps, where each intermediate step produces not just a single point estimate, but a cost function over multiple solutions, which reduces the information loss at each processing step. We conclude with examples from a clinical trial, where the fields of cardiac arrhythmias are presented as two-dimensional contour plots.

In this paper, the design flexibility of the control-bounded analog-to-digital converter principle is demonstrated. A band-pass analog-to-digital converter is considered as an application and case study. We show how a low-pass control-bounded analog-to-digital converter can be translated into a band-pass version where the guaranteed stability, converter bandwidth, and signal-to-noise ratio are preserved while the center frequency for conversion can be positioned freely. The proposed converter is validated with behavioral simulations on several filter orders, center frequencies, and oversampling ratios. Additionally, we consider an op-amp circuit realization where the effects of first-order op-amp non-idealities are shown. Finally, robustness against component variations is demonstrated by Monte Carlo simulations.