A robust and memory-efficient spectrogram representation for respiratory signals based on quasi-random sampling and Hilbert folding

Analyzing non-stationary respiratory sounds requires capturing brief, high-frequency acoustic transients. However, standard high-resolution time-frequency representations exhibit significant temporal redundancy and impose memory constraints for edge-based deployment, while traditional downsampling methods often omit or alias transient biomarkers. To address this redundancy-fidelity problem, we propose MelHilbertLDS, a lightweight acoustic feature representation framework. The method integrates quasi-random temporal downsampling via Low-Discrepancy Sequences (LDS) with spatial structuring using generalized Hilbert space-filling curves. LDS minimizes discrepancy bounds to provide principled coverage of transient events, acting as a temporal regularizer. Hilbert folding translates 1D temporal proximity into 2D spatial adjacency, which expands the effective receptive field of convolutional neural networks (CNNs) and compresses spatial dimensions. We evaluated the framework across three acoustic datasets, covering controlled event detection, data-scarce environments, and noisy clinical recordings. Results show that MelHilbertLDS reduces performance variance in low-resource scenarios and improves training stability. It achieves up to a 50-fold reduction in activation memory, a 44% reduction in CPU inference latency on MobileNetV3, and a 96% reduction in FLOPs on high-capacity CNNs, while maintaining competitive diagnostic performance. MelHilbertLDS offers a promising approach for automated analysis of transient acoustic events under memory constraints.