The Surprising Benefits of Hysteresis in Unlimited Sampling: Theory, Algorithms and Experiments

  title={The Surprising Benefits of Hysteresis in Unlimited Sampling: Theory, Algorithms and Experiments},
  author={Dorian Florescu and Felix Krahmer and Ayush Bhandari},
  journal={IEEE Transactions on Signal Processing},
The Unlimited Sensing Framework (USF) was recently introduced to overcome the sensor saturation bottleneck in conventional digital acquisition systems. At its core, the USF converts a continuous-time high-dynamic-range (HDR) signal into folded, low-dynamic-range, modulo samples and allows the recovery of the HDR signal via algorithmic unfolding. In hardware, however, implementing ideal modulo folding requires careful calibration, analog design and high precision. At the interface of theory and… 

Figures and Tables from this paper


On Unlimited Sampling and Reconstruction
An alternative paradigm for sensing and recovery, called the Unlimited Sampling Framework, which derives conditions when perfect recovery is possible and complement them with a stable recovery algorithm and guarantees extend to measurements affected by bounded noise, which includes round-off quantization.
Unlimited Sampling From Theory to Practice: Fourier-Prony Recovery and Prototype ADC
This paper studies the problem of recovering a bandlimited signal from point-wise modulo samples, aiming to connect theoretical guarantees with hardware implementation considerations, and provides a new Fourier domain recovery algorithm.
One-bit Unlimited Sampling
  • Olga Graf, A. Bhandari, F. Krahmer
  • Computer Science
    ICASSP 2019 - 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
  • 2019
This paper provides a constructive recovery algorithm for bandlimited signals from one-bit modulo samples complemented with a bound on the reconstruction error and shows that the scheme overcomes the dynamic range limitations of conventional one- bit quantizer.
Unlimited Sampling of Sparse Sinusoidal Mixtures
This paper develops a method for recovery of $K-sparse, sum-of-sinusoids from finitely many wrapped samples, thus avoiding clipping or saturation, and obtains a parametric sampling theorem.
Unlimited Sampling of Sparse Signals
A new sparse sampling theorem is written and an algorithm which stably recovers a sparse signal from low-pass, modulo samples is developed which allows for perfect recovery of a bandlimited function whose amplitude exceeds the ADC threshold by orders of magnitude.
Wavelet-Based Reconstruction for Unlimited Sampling
This work considers the problem of recovering the original signal from the measured modulo-operated signal and derives a sufficient condition on the sampling frequency for ensuring perfect reconstruction of the smooth signal.
On unlimited sampling
Numerical experiments that corroborate the theory indeed show that it is possible to perfectly recover function that takes values that are orders of magnitude higher than the ADC's threshold, and prove such sufficiency conditions and complement them with a stable recovery algorithm.
Event-Driven Modulo Sampling
This work proposes a cascade model comprising a modulo non-linearity in series with an integrate-and-fire (IF) event-driven encoder and introduces theoretical conditions for which the input of the proposed cascade model can be recovered with arbitrary precision.
A Digitally Assisted, Signal Folding Neural Recording Amplifier
  • Yi Chen, A. Basu, M. Je
  • Engineering
    IEEE Transactions on Biomedical Circuits and Systems
  • 2014
A novel signal folding and reconstruction scheme for neural recording applications that exploits the 1/fn characteristics of neural signals is described in this paper, which enables the use of an analog-to-digital convertor with less number of bits for the same effective dynamic range.
Computational Array Signal Processing via Modulo Non-Linearities
This work proposes “computational arrays” which are based on a co-design approach so that a collaboration between the sensor array hardware and algorithms can be harnessed and introduces a new form of information loss in terms of the modulo measurements.