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GPU-Accelerated Adaptive Chirplet Transform (ACT)

Real-time non-stationary signal decomposition using an adaptive chirplet dictionary, accelerated via a hybrid CPU-GPU pipeline for large-scale runtime analysis.

View Repository Related Publication arXiv Preprint

The animation below shows a real decomposition on 2 seconds of EEG (512 samples at 256 Hz) from channel 1, one of two frontal electrodes, of Patient 1 in the Bitbrain sleep EEG dataset. Watch the approximation build up and the residual shrink as each chirplet is added; by the final chirplet, residual energy drops to about 4% of the original signal. Full technical breakdown below the animation.

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How It Works

The Problem

The Adaptive Chirplet Transform decomposes a non-stationary signal into a small set of time–frequency atoms, each fit greedily via matching pursuit to explain as much of the remaining signal energy as possible. It has been applied to EEG, EMG, and radar signals, but two issues have historically blocked real deployment:

  1. Algorithmic instability. The per-step search for the best-fit chirplet happens over a high-dimensional, non-convex parameter space. Without careful numerical treatment, the decomposition can diverge, and later steps make the residual worse, not better.
  2. Computational cost. Searching that parameter space naively is too slow for real-time use, ruling out on-device and wearable applications where speed is a hard constraint.

The Approach

Math: unit-normalized, residual-based projection. The core change is aligning the per-step projection strictly with Matching Pursuit theory by normalizing the chirplet basis at each iteration and projecting against the true residual, rather than a looser approximation of it. This eliminates divergence and substantially reduces residual error, and the effect holds across signal domains, not just EEG.

Architecture: hybrid CPU–GPU pipeline. Chirplet generation (constructing candidate atoms from the parameter space) runs on the CPU. The search over those candidates, which is the expensive part, is parallelized on the GPU. Splitting the work this way removes the bottlenecks of doing either step alone: CPU-only search is too slow; GPU-only generation doesn't parallelize well.

Pipeline architecture
EEG Epoch 512 samples, 256 Hz CPU Candidate Generation chirplet dictionary GPU Parallel Search unit-normalized projection Atom k best-fit chirplet Residual Update subtract atom from signal loop ×12

Chirplet generation runs on the CPU; the expensive parallel search over candidates runs on the GPU. Each iteration's residual feeds back into the next candidate search.

Seeing It Work

On the real EEG epoch animated above, the decomposition converges cleanly: after 1 chirplet, roughly 43% of signal energy remains unexplained; after 12 chirplets, that residual drops to about 4.3%. Each added chirplet explains a diminishing but consistent share of what's left of the signal, no divergence, no wasted steps.

Status & Citation

Under review at IEEE Open Journal of Signal Processing (submitted July 2026). Full derivation, benchmarks, and multi-channel scalability results are in the paper — N. Kumar, S. Mann, “Toward a Stable and Deployable Adaptive Chirplet Transform: Residual Projection, Hybrid GPU Acceleration, and Multi-Channel Scalability”, arXiv:2607.16629, 2026.

BibTeX Citation

@article{kumar2026chirplet,
  title={Toward a Stable and Deployable Adaptive Chirplet Transform: Residual Projection, Hybrid GPU Acceleration, and Multi-Channel Scalability},
  author={Kumar, Nishant and Mann, Steve},
  journal={arXiv preprint arXiv:2607.16629},
  year={2026}
}