# Time Encoding of Finite-Rate-of-Innovation Signals

arXiv: https://arxiv.org/abs/2107.03344 · HTML: https://mlsanity.com/paper/2107.03344/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Jul 2021.

## Built on by (most cited first, 2 of 2)

- [A Time Encoding approach to training Spiking Neural Networks](https://mlsanity.com/paper/2110.06735/) (2021)
- [Time Encoding Quantization of Bandlimited and Finite-Rate-of-Innovation Signals](https://mlsanity.com/paper/2110.01928/) (2021)

## Abstract (arXiv)

Time-encoding of continuous-time signals is an alternative sampling paradigm to conventional methods such as Shannon's sampling. In time-encoding, the signal is encoded using a sequence of time instants where an event occurs, and hence fall under event-driven sampling methods. Time-encoding can be designed agnostic to the global clock of the sampling hardware, which makes sampling asynchronous. Moreover, the encoding is sparse. This makes time-encoding energy efficient. However, the signal representation is nonstandard and in general, nonuniform. In this paper, we consider time-encoding of finite-rate-of-innovation signals, and in particular, periodic signals composed of weighted and time-shifted versions of a known pulse. We consider encoding using both crossing-time-encoding machine (C-TEM) and integrate-and-fire time-encoding machine (IF-TEM). We analyze how time-encoding manifests in the Fourier domain and arrive at the familiar sum-of-sinusoids structure of the Fourier coefficients that can be obtained starting from the time-encoded measurements via a suitable linear transformation. Thereafter, standard FRI techniques become applicable. Further, we extend the theory to multichannel time-encoding such that each channel operates with a lower sampling requirement. We also study the effect of measurement noise, where the temporal measurements are perturbed by additive noise. To combat the effect of noise, we propose a robust optimization framework to simultaneously denoise the Fourier coefficients and estimate the annihilating filter accurately. We provide sufficient conditions for time-encoding and perfect reconstruction using C-TEM and IF-TEM, and furnish extensive simulations to substantiate our findings.