| name | spiking-bandpass-wavelet-encoding |
| description | Spiking Bandpass Wavelet encoding methodology for temporal signal processing. Recasts spike encoders as time-causal wavelet frames with quantitative bandwidths and reconstruction error bounds. Maps spike representations to signal processing theory, enabling neuromorphic hardware implementation. Applicable to SNN temporal encoding, neuromorphic signal processing, event-based sensing, ECG/audio processing with spiking networks. Activation: spiking wavelet, spike encoding, temporal signal encoding, bandpass wavelet, neuromorphic signal processing, spike-based encoding, time-causal wavelets, ECG spiking, audio spiking, spike reconstruction
|
Spiking Bandpass Wavelet Encoding
Based on: Pedersen, Lindeberg & Gerstoft (2026) arXiv:2605.09770
Core Insight
Spike-based encodings are typically formulated probabilistically, disconnected from
signal processing theory. This work recasts spike encoders as time-causal wavelet frames
with:
- Quantitative bandwidth specifications
- Reconstruction error bounds
- Direct mapping to neuromorphic hardware
Theoretical Framework
Spike Encoder as Wavelet Frame
A spike encoder produces events when the signal crosses a threshold. This can be
reformulated as a wavelet transform where:
- Basis functions: Bandpass wavelets derived from the spike generation mechanism
- Time-causality: Each wavelet depends only on past signal values
- Sparsity: Natural sparsity from the spike threshold mechanism
- Locality: Each spike encodes local signal features
Reconstruction
Signal reconstruction from spikes is possible up to:
- Spike quantization error
- Time discretization error
Achieves normalized RMSE comparable to continuous wavelet transforms.
Implementation Pattern
import numpy as np
class SpikingWaveletEncoder:
"""Encode temporal signals using spiking bandpass wavelets."""
def __init__(self, n_channels, bandwidth, sample_rate):
self.n_channels = n_channels
self.bandwidth = bandwidth
self.sample_rate = sample_rate
self.filters = self._build_wavelet_filters()
def _build_wavelet_filters(self):
"""Construct bandpass wavelet filters for each channel."""
filters = []
for i in range(self.n_channels):
center_freq = self.bandwidth * (2 ** i)
t = np.arange(0, 100) / self.sample_rate
wavelet = np.exp(-t * center_freq) * np.sin(2 * np.pi * center_freq * t)
wavelet = wavelet / np.sum(wavelet**2)
filters.append(wavelet)
return np.array(filters)
def encode(self, signal):
"""Encode signal as spike train via wavelet thresholding."""
spikes = []
for filt in self.filters:
response = np.convolve(signal, filt, mode='same')
threshold = np.std(response) * 0.5
spike_times = np.where(np.diff(np.sign(response - threshold)) > 0)[0]
spikes.append(spike_times)
return spikes
def decode(self, spikes, original_length):
"""Reconstruct signal from spike train."""
reconstruction = np.zeros(original_length)
for i, spike_times in enumerate(spikes):
for t in spike_times:
if t < len(self.filters[i]):
reconstruction[t:t+len(self.filters[i])] += self.filters[i]
return reconstruction
Key Properties
| Property | Description |
|---|
| Sparsity | Only fires when signal exceeds local threshold |
| Energy efficiency | Sparse spike events minimize computation |
| Time-causal | No future information needed |
| Bandwidth control | Adjustable frequency coverage per channel |
| Hardware mapping | Direct implementation on neuromorphic chips |
Applications
- ECG signal processing with spiking networks
- Audio feature extraction for neuromorphic hearing
- Event-based vision sensor preprocessing
- Temporal signal compression
- Real-time anomaly detection in streaming data
Advantages Over Traditional Encodings
- Signal processing connection: Bridges spike coding and wavelet theory
- Reconstruction guarantees: Error bounds on signal recovery
- Neuromorphic compatibility: Maps directly to event-based hardware
- No probabilistic assumptions: Deterministic wavelet formulation
Related Skills
cortico-cerebellar-modularity-rnn - Brain-inspired RNN architecture
spikingjelly-framework - SNN deep learning framework
snn-performance-analysis - SNN performance evaluation
edgespike-edge-iot-snn - Edge SNN deployment
ArXiv Reference
- Paper: arXiv:2605.09770v1
- Title: Encoding and Decoding Temporal Signals with Spiking Bandpass Wavelets
- Authors: Jens Egholm Pedersen, Tony Lindeberg, Peter Gerstoft
- Date: 2026-05-10
- Categories: cs.NE, eess.SP, q-bio.NC