Phase encoding and time-frequency analysis in polar coordinates for spiking neural network design

This paper presents a novel phase encoding scheme for spike trains in Spiking Neural Networks (SNNs) inspired by Fourier series and the Discrete Fourier Transform (DFT). The proposed method leverages complex exponential spiking neurons to represent frequency components, allowing for the efficient reconstruction of original time signals. We explore the time shifting property of the Fourier transform to demonstrate how time delays in impulse signals can be encoded as phase shifts in the frequency domain. Detailed mathematical formulations and illustrative examples highlight the relationship between impulse delays and phase patterns in SNNs. The primary objective of this research is to develop a streamlined and computationally efficient SNN architecture, enhancing the training process. Future work will expand this phase encoding method to various sequence patterns, aiming to improve the performance and versatility of SNNs in neuromorphic computing for complex information processing tasks. The results indicate that this approach holds promise for advancing the field by providing a robust framework for precise signal reconstruction and efficient neural network design.