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.

翻译：基于脉冲的编码具有稀疏性和能效性，但大多以概率形式构建，与主流信号处理文献脱节。我们将脉冲编码器重构为具有定量带宽和重建误差界的时间因果小波框架。所提出的小波保留了脉冲表示的稀疏性和局部性，重建误差仅受限于脉冲量化和时间离散化。我们在心电信号和音频数据集上进行了重建实验，实现了与连续小波变换相当的归一化均方根误差。这些脉冲小波可直接映射至神经形态硬件。