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Adaptive Non-Uniform Sampling of Bandlimited Signals via Algorithm-Encoder Co-Design

Kaluguri Yashaswini, Anshu Arora, Satish Mulleti

TL;DR

A variable-bias, variable-threshold integrate-and-fire time encoding machine (VBT-IF-TEM) whose firing mechanism is explicitly shaped to enforce the derived local convergence condition, which achieves substantial reductions in sampling density compared to uniform sampling and conventional IF-TEMs, while maintaining accurate reconstruction.

Abstract

We propose an adaptive non-uniform sampling framework for bandlimited signals based on an algorithm-encoder co-design perspective. By revisiting the convergence analysis of iterative reconstruction algorithms for non-uniform measurements, we derive a local, energy-based sufficient condition that governs reconstruction behavior as a function of the signal and derivative energies within each sampling interval. Unlike classical approaches that impose a global Nyquist-type bound on the inter-sample spacing, the proposed condition permits large gaps in slowly varying regions while enforcing denser sampling only where the signal exhibits rapid temporal variation. Building on this theoretical insight, we design a variable-bias, variable-threshold integrate-and-fire time encoding machine (VBT-IF-TEM) whose firing mechanism is explicitly shaped to enforce the derived local convergence condition. To ensure robustness, a shifted-signal formulation is introduced to suppress excessive firing in regions where the magnitude of the signal amplitude is close to zero or the local signal energy approaches zero. Using the proposed encoder, an analog signal is discretely represented by time encodings and signal averages, enabling perfect reconstruction via a standard iterative algorithm even when the local sampling rate falls below the Nyquist rate. Simulation results on synthetic signals and experiments on ultrasonic guided-wave and ECG signals demonstrate that the proposed framework achieves substantial reductions in sampling density compared to uniform sampling and conventional IF-TEMs, while maintaining accurate reconstruction. The results further highlight a controllable tradeoff between sampling density, reconstruction accuracy, and convergence behavior, which can be navigated through adaptive parameter selection.

Adaptive Non-Uniform Sampling of Bandlimited Signals via Algorithm-Encoder Co-Design

TL;DR

A variable-bias, variable-threshold integrate-and-fire time encoding machine (VBT-IF-TEM) whose firing mechanism is explicitly shaped to enforce the derived local convergence condition, which achieves substantial reductions in sampling density compared to uniform sampling and conventional IF-TEMs, while maintaining accurate reconstruction.

Abstract

We propose an adaptive non-uniform sampling framework for bandlimited signals based on an algorithm-encoder co-design perspective. By revisiting the convergence analysis of iterative reconstruction algorithms for non-uniform measurements, we derive a local, energy-based sufficient condition that governs reconstruction behavior as a function of the signal and derivative energies within each sampling interval. Unlike classical approaches that impose a global Nyquist-type bound on the inter-sample spacing, the proposed condition permits large gaps in slowly varying regions while enforcing denser sampling only where the signal exhibits rapid temporal variation. Building on this theoretical insight, we design a variable-bias, variable-threshold integrate-and-fire time encoding machine (VBT-IF-TEM) whose firing mechanism is explicitly shaped to enforce the derived local convergence condition. To ensure robustness, a shifted-signal formulation is introduced to suppress excessive firing in regions where the magnitude of the signal amplitude is close to zero or the local signal energy approaches zero. Using the proposed encoder, an analog signal is discretely represented by time encodings and signal averages, enabling perfect reconstruction via a standard iterative algorithm even when the local sampling rate falls below the Nyquist rate. Simulation results on synthetic signals and experiments on ultrasonic guided-wave and ECG signals demonstrate that the proposed framework achieves substantial reductions in sampling density compared to uniform sampling and conventional IF-TEMs, while maintaining accurate reconstruction. The results further highlight a controllable tradeoff between sampling density, reconstruction accuracy, and convergence behavior, which can be navigated through adaptive parameter selection.
Paper Structure (15 sections, 3 theorems, 35 equations, 10 figures, 1 table)

This paper contains 15 sections, 3 theorems, 35 equations, 10 figures, 1 table.

Table of Contents

  1. Introduction
  2. Adaptive Non-Uniform Sampling Approach
  3. Iterative Reconstruction and Convergence Analysis
  4. Variable-Bias-Threshold IF-TEM
  5. VBT-IF-TEM with Biased Signal
  6. Proposed Adaptive Non-Uniform Sampling
  7. Related Work
  8. Simulation Results
  9. Chirp Signal
  10. Sum-of-Sincs Signal
  11. Adaptive Selection of $\alpha$ and $\beta$
  12. Practical Applications
  13. Ultrasonic Guided-Wave Signals
  14. ECG Signals
  15. Conclusion

Key Result

Theorem 1

Let $f(t) \in \mathcal{B}_{\Omega_0, c}$ be a bandlimited signal. Consider a variable-bias-threshold IF-TEM sampling as shown in Fig. fig:general-TEM. The signal can be perfectly reconstructed from the time encodings $\{t_n\}$ generated by the approach, provided that the bias and thresholds are chos where $\alpha \in (0,1)$ and $\beta > 0$ are user-defined positive scalars.

Figures (10)

  • Figure 1: Framework of the proposed VBT-IF-TEM
  • Figure 2: A comparison of firings of VBT-IF-TEMs (a) without shift -- 396 firings, and (b) with shift -- 51 firings.
  • Figure 3: Different firing rates in different regions
  • Figure 4: Comparison of different sampling schemes for a chirp-like signal. The proposed Adaptive-NUS produces fewer samples and achieves sub-Nyquist sampling in low-activity regions.
  • Figure 8: Comparison of different sampling schemes for a SoS signal with multiple bandwidth regions. The proposed Adaptive-NUS produces fewer samples and achieves sub-Nyquist sampling in low-activity regions.
  • ...and 5 more figures

Theorems & Definitions (7)

  • Theorem 1
  • proof
  • Remark 1
  • Remark 2
  • Theorem 2
  • proof
  • Theorem 3: Adaptive Non-Uniform Sampling