Scale covariant and spiking wavelets

Wavelets that are guaranteed to be scale covariant, implemented as standard transforms and with spiking neurons.

Why

Standard wavelets are excellent at robust signal processing but work offline: they need the full signal. Real-time streams (audio, biosignals, sensors) need causal wavelets, and signals at unpredictable rates benefit from scale covariance: the response transforms predictably under time rescaling.

swavelet contains time-causal wavelets that can be used directly as neuromorphic signal encoders, deployable directly to neuromorphic hardware via NIR, both as spiking and non-spiking variants.

The spiking variants double as event-driven ADCs, encoding continuous inputs straight into sparse spike trains, skipping the uniform sampler entirely.

Usage

Install via uv: uv add swavelet or via pip: pip install swavelet

Encoding and decoding (non-spiking)

import jax.numpy as jnp
from swavelet import DoT

dt = 1e-3                        # Simulation time delta
t = jnp.arange(0, 1.0, dt)       # Duration: 1 second
signal = jnp.sin(2 * jnp.pi * t) # A simple sinusoidal

w = DoT(n_channels=4, dt=dt, mu_max=0.05) # 4-channel wavelet
coeffs = w(w.params, signal)              # analysis: (n_channels, T)
recon = w.reconstruct(w.params, coeffs)   # synthesis: back to signal

Encoding and decoding (spiking)

The same shape works for every wavelet — call returns coefficients, reconstruct inverts them. Spiking variants substitute spike trains for coefficients:

from swavelet import SpikingDoT

w = SpikingDoT(n_channels=4, dt=dt, mu_max=0.05)
spikes = w(w.params, signal) # (2 * n_channels, T)
# Use the spikes in your ML pipeline or reconstruct:
recon  = w.reconstruct(w.params, spikes)

Export to NIR

import nir
from swavelet import SpikingDoE

w = SpikingDoE(n_channels=4, dt=dt, mu_max=0.05)
nir_graph = w.to_nir()
nir.write("spiking_doe.nir", nir_graph)

The graph is a single chain: a fanout Affine broadcasts the scalar input across the K smoothing channels, the multi-channel LI bank produces L_1..L_K, the connectivity Affine wires each bandpass row with ±1 weights between adjacent scales (and the lowpass row taps L_K directly), and a multi-channel LIF emits the spike output. Diagram via NirViz:

Wavelet implementations (spiking and non-spiking)

• DoG: Difference of Gaussian
• DoT: Difference of time-causal limit kernel
• DoE: Difference of truncated exponential (DoT with cascade depth=1)

Acknowledgements

Please cite our paper:

@inproceedings{pedersen2026scalecovariant,
  title = {Scale-{{Covariant Spiking Wavelets}}},
  booktitle = {2026 {{IEEE International Conference}} on {{Acoustics}}, {{Speech}} and {{Signal Processing}} ({{ICASSP}})},
  author = {Pedersen, Jens Egholm and Lindeberg, Tony and Gerstoft, Peter},
  year = 2026,
  month = may,
  pages = {20347--20351},
  issn = {2379-190X},
  doi = {10.1109/ICASSP55912.2026.11463688},
  urldate = {2026-05-10},
}