Time Encoding Sampling of Bandpass Signals

TL;DR

This paper explores sampling and reconstruction of bandpass signals using time encoding machines, demonstrating equivalence to non-uniform sampling and providing conditions for perfect recovery based on TEM parameters.

Contribution

It introduces a novel TEM-based sampling scheme for bandpass signals, linking TEM parameters to signal bandwidth and amplitude for accurate reconstruction.

Findings

TEM sampling is equivalent to periodic non-uniform sampling.

Perfect reconstruction is possible when TEM parameters satisfy specific bounds.

Numerical experiments confirm the scheme's effectiveness.

Abstract

This paper investigates the problem of sampling and reconstructing bandpass signals using time encoding machine(TEM). It is shown that the sampling in principle is equivalent to periodic non-uniform sampling (PNS). Then the TEM parameters can be set according to the signal bandwidth and amplitude instead of upper-edge frequency and amplitude as in the case of bandlimited/lowpass signals. For a bandpass signal of a single information band, it can be perfectly reconstructed if the TEM parameters are such that the difference between any consecutive values of the time sequence in each channel is bounded by the inverse of the signal bandwidth. A reconstruction method incorporating the interpolation functions of PNS is proposed. Numerical experiments validate the feasibility and effectiveness of the proposed TEM scheme.