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Classical sampling is based on acquiring signal amplitudes at specific points in time, with the minimal sampling rate dictated by the degrees of freedom in the signal. The samplers in this framework are controlled by a global clock that operates at a rate greater than or equal to the minimal sampling rate. At high sampling rates, clocks are power-consuming and prone to electromagnetic interference. An integrate-and-fire time encoding machine (IF-TEM) is an alternative power-efficient sampling mechanism which does not require a global clock. Here, the samples are irregularly spaced threshold-based samples. In this paper, we investigate the problem of sampling finite-rate-ofinnovation (FRI) signals using an IF-TEM. We provide theoretical recovery guarantees for an FRI signal with arbitrary pulse shape and without any constraint on the minimum separation between the pulses. In particular, we show how to design a sampling kernel, IF-TEM, and recovery method such that the FRI signals are perfectly reconstructed. We then propose a modification to the sampling kernel to improve noise robustness. Our results enable designing low-cost and energy-efficient analogto-digital converters for FRI signals.

The inverse kinematics problem deals with the question of how the nervous system coordinates movement to resolve redundancy, such as in the case of arm reaching movements where more degrees of freedom are available at the joint versus hand level. In particular, this work focuses on determining which coordinate frames can best represent human movements, allowing the motor system to solve the inverse kinematics problem in the presence of kinematic redundancies. In particular, in this work we used a multi-dimension sparse source separation method called FADA to derive sets of basis functions (here called sources) for both the task and joint spaces, with joint space being represented in terms of either the absolute or anatomical joint angles. We assessed the similarities between the joint and task sources in each of these joint representations. We found that the time-dependent profiles of the absolute reference frame's sources show greater similarity to those of the corresponding sources in the task space. This result was found to be statistically significant. Hence, our analysis suggests that the nervous system represents multi-joint arm movements using a limited number of basis functions, to allow for simple transformations between task and joint spaces. Importantly, joint space seems to be represented in terms of an absolute reference frame to achieve successful performance and simplify inverse kinematics transformations in the face of the existing kinematic redundancies. Further studies will be needed to determine the generalizability of this finding and its implications concerning neural control of movement.

No abstract

Analog-to-digital converters (ADCs) are key components of digital signal processing. Classical samplers in this framework are controlled by a global clock. At high sampling rates, clocks are expensive and power-hungry, thus increasing the cost and energy consumption of ADCs. It is, therefore, desirable to sample using a clock-less ADC at the lowest possible rate. An integrate-and-fire time-encoding machine (IF-TEM) is a timebased power-efficient asynchronous design that is not synced to a global clock. Finite-rate-of-innovation (FRI) signals, ubiquitous in various applications, have fewer degrees of freedom than the signal's Nyquist rate, enabling sub-Nyquist sampling signal models. This work proposes a power-efficient IF-TEM ADC architecture and demonstrates sub-Nyquist sampling and FRI signal recovery. Using an IF-TEM, we implement in hardware the first sub-Nyquist time-based sampler. We offer a feasible approach for accurately estimating the FRI parameters from IF-TEM data. The suggested hardware and reconstruction approach retrieves FRI parameters with an error of up to -25dB while operating at rates approximately 10 times lower than the Nyquist rate, paving the way to low-power ADC architectures.Index Terms-Brain-inspired computing, analog-to-digital conversion (ADC), time-based sampling hardware, integrate and fire TEM (IF-TEM), sub-Nyquist sampling, finite-rate-of innovation (FRI) signals.