We present Q-transform amplitude modulation (qtam), a novel, fully invertible implementation of the constant-Q transform (CQT) algorithm, designed to enable robust signal denoising and the disentanglement of overlapping transient events in current and, especially, next generation gravitational wave observatories. Conventional time-frequency (TF) analysis faces a fundamental dichotomy: critically sampled transforms (e.g., standard discrete wavelets) are computationally efficient but lack time-shift equivariance, limiting their efficacy for robust pattern recognition and deep learning applications. While alternative approaches such as the dual-tree complex wavelet transform provide efficient approximate shift invariance, their wavelet constructions remain tied to dyadic scale frequency tilings that are poorly matched to the simultaneous representation of compact binary chirps and instrumental glitches. Scattering transforms further improve translation stability, but do so through nonlinear modulus and averaging operations that sacrifice phase coherence and are not designed for exact signal reconstruction. Conversely, overcomplete transforms (e.g., standard CQT or stationary wavelets) provide the necessary shift-equivariance and tunable frequency resolution, but their implementations generate highly redundant data volumes that are prohibitive for low-latency processing. Furthermore, standard attempts to compress these dense representations rely on lossy interpolation or magnitude-only reduction, destroying the phase coherence required to reconstruct the time-domain signal. qtam bridges this gap by employing a methodology inspired by amplitude modulation radio broadcasting. By modeling the Q-transform output as a slowly varying complex envelope carried by a known deterministic high-frequency term, we achieve lossless data decimation via spectral shifting to baseband. We demonstrate that qtam is linear and fully invertible, allowing exact reconstruction of the original time-series signal with machine precision while retaining the shift-equivariance of dense spectrograms. Leveraging native graphics processing unit acceleration (pytorch), qtam achieves speedups of approximately two orders of magnitude with respect to standard implementations, enabling high-fidelity TF pipelines to operate within strict low-latency [$\mathcal{O}(1s)$] bounds. We validate the method’s potential for denoising and disentanglement through tests on real gravitational wave data and simulated signal injections.

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• Gravitational waves
• Time series analysis