Hardware

To perform the modulo operation in the analog domain, a Modulo Analog-to-Digital Converter (MADC) is designed to digitize high-dynamic-range (HDR) signals by applying a modulo operation to the input signal prior to digitization. This approach effectively mitigates common challenges such as clipping and saturation found in traditional ADCs by folding signals that exceed a specified amplitude threshold (\(\lambda\)) [11].

Modulo Folding: When the amplitude of the input signal surpasses the threshold \(\lambda\), the MADC “folds” the signal back into the range \([-\lambda, \lambda]\). In other words, the ADC output represents the remainder of the input signal after division by \(2\lambda\). This folding operation compresses HDR signals into a manageable low-dynamic-range (LDR) format, facilitating digitization without saturation while preserving the original signal’s information for accurate reconstruction.

\[\newcommand{\MO}{\mathscr{M}_\lambda} \newcommand{\ft}[1]{\left[\kern-0.15em\left[#1\right]\kern-0.15em\right]} \newcommand{\fe}[1]{\left[\kern-0.30em\left[#1\right]\kern-0.30em\right]} \newcommand{\flr}[1] {\left\lfloor #1 \right\rfloor} \def\DE{\stackrel{\rm{def}}{=}} \begin{equation} \MO: g \to 2\lambda \left( {\fe{ {\frac{g}{{2\lambda }} + \frac{1}{2} } } - \frac{1}{2} } \right), \ \ \ft{g} \DE g - \flr{g} \label{eq1} \end{equation}\]

The Modulo folding operation will result a radically different ADC transfer function (left) than the traditional ADC (right). For input voltages higher than λ, all the information is lost due to saturation, while all the information preserved by modulo folding.

The MADC hardware enables the development of acquisition systems capable of supporting various applications, such as Multi-Channel systems and Event-Driven processing. These applications benefit from the enhanced dynamic range and resilience to high-amplitude signals provided by the modulo ADC approach.