Toward a Stable and Deployable Adaptive Chirplet Transform: Residual Projection, Hybrid GPU Acceleration, and Multi-Channel Scalability

The Adaptive Chirplet Transform is a flexible framework that can decompose non-stationary signals into sparse chirplets; it has been applied to signals such as electroencephalography, electromyography and radar. However, the practical deployment of this transform has been hindered by two challenges: algorithmic instability in prior implementations, which can lead to divergent decompositions, and the computational cost of searching over a high-dimensional parameter space. This paper addresses both by a sequence of contributions. Firstly, unit normalization and residual-based projection are introduced to align the decomposition with Matching Pursuit Theory, thereby eliminating divergence and substantially reducing residual error across all signal domains, as demonstrated on three representative signal types. A hybrid CPU-GPU architecture offloads chirplet family generation to the CPU while parallelizing the search on the GPU, removing bottlenecks in CPU-only search and GPU-only generation, achieving speedups of 6.6-7.38 on desktop hardware, with consistent gains observed across laptop and embedded platforms. Multichannel batching enabled simultaneous multi-signal processing, amplifying the speedup, which scaled from 3.94 for a single channel to 8.22 at 10 channels. Finally, a hierarchical coarse-to-fine search, inspired by Logon Expectation Maximization, is introduced. This reduced peak memory usage below 1 GB while maintaining similar reconstruction quality, at the cost of longer runtime. Together, these contributions establish a correct, stable and practically deployable foundation for chirplet-based signal decomposition. Index Terms: Chirplet Transform, GPU Computing, Matching Pursuit, Signal Decomposition, Sparse Representation, Time-Frequency Analysis