Encoding and Decoding Temporal Signals with Spiking Bandpass Wavelets

2026-05-10

AI Summary

This work addresses the limitations of traditional spike coding methods, which often rely on probabilistic models and lack compatibility with mainstream signal processing theory, making it difficult to define bandwidth and guarantee reconstruction fidelity. The authors propose a novel spike coding framework grounded in causal temporal wavelets, introducing for the first time a bandwidth-controllable wavelet representation into spike coding to achieve sparse, localized, and reconstructable spiking representations of temporal signals. By integrating causal bandpass wavelet frames, spike-based quantization, and temporal discretization, the method provides rigorous theoretical bounds on reconstruction error. Experimental results demonstrate that, on ECG and audio signals, the proposed approach achieves normalized root-mean-square errors comparable to those of the continuous wavelet transform while remaining amenable to deployment on neuromorphic hardware.

Abstract

Spike-based encodings are sparse and energy-efficient, but have largely been formulated probabilistically, disconnected from most signal processing literature. We recast spike encoders as time-causal wavelet frames with quantitative bandwidths and reconstruction error bounds. The proposed wavelets preserve the sparsity and locality of spiking representations, with reconstruction up to spike quantization and time discretization. We demonstrate reconstruction on ECG and audio datasets, achieving a normalized RMSE comparable to continuous wavelet transforms. The spiking wavelets map directly to neuromorphic hardware.

Problem

• spiking encoding
• temporal signals
• wavelet frames
• signal reconstruction
• neuromorphic hardware

Innovation

• spiking wavelets
• time-causal wavelet frames
• sparse encoding
• neuromorphic hardware
• signal reconstruction