Encoding and Decoding Temporal Signals with Spiking Bandpass Wavelets

TL;DR

This paper introduces a novel wavelet-based encoding and decoding framework for spike-based signals, enabling efficient reconstruction of ECG and audio data with theoretical guarantees and hardware compatibility.

Contribution

It reformulates spike encoders as time-causal wavelet frames with explicit bandwidth and error bounds, bridging signal processing and neuromorphic hardware.

Findings

Achieved ECG and audio reconstruction with normalized RMSE comparable to continuous wavelet transforms.

Reconstruction is effective up to spike quantization and time discretization.

Wavelet framework maps directly to neuromorphic hardware implementations.

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.