Time-Based Finite-Rate-of-Innovation Sampling for Variable-Pulse-Width Signal

The finite-rate-of-innovation (FRI) sampling method can reconstruct signals with few samples. However, classical FRI sampling often has serious model mismatch when dealing with asymmetric pulse signals. The variable-pulse-width (VPW) signal model is composed of asymmetric pulses with variable width, which can better match the asymmetric pulse signals in the actual signal measurement, such as electrocardiogram (ECG) and bidirectional reflectance distribution function (BRDF). The VPW-FRI sampling theory provides an effective alternative to sub-Nyquist sampling of such signals. Recent studies have used time encoding machine (TEM), an alternative sampling scheme, to replace the analog-to-digital converter in classical FRI frameworks. Such devices acquire signal samples through time measurement rather than measuring the intensity, with lower power consumption and less electronic interference. However, the existing TEM-FRI sampling methods do not match the VPW signal model. In this article, a sampling method based on TEM-FRI sampling scheme for VPW signals is proposed. We extend the signal model of TEM-FRI sampling framework to VPW signal, and give the mathematical derivation of the perfect reconstruction for VPW signal based on TEM-FRI sampling method. For the VPW signal containing K pulses, our method can guarantee the perfect reconstruction of VPW signals when the number of samples
N
≥ 4
K
+ 1 in one signal period. And we present a robust reconstruction algorithm by denoising samples in the frequency domain, the simulation results show that our proposed method is more robust than classical FRI sampling method in the presence of noise. In addition, we present a TEM-based FRI sampling hardware system, and explain how to implement the sampling kernel in our harware system with an analog filter device. According to the experiments, the TEM-FRI hardware system can sample and reconstruct the VPW signal.