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Fungal electrical activity exhibits spikes and slow oscillatory modulations over seconds to hours. We introduce a √t-warped wave transform that concentrates long-time structure into compact spectral peaks, improving time-frequency localization for sublinear temporal dynamics. On open fungal datasets (fs≈1 Hz) the method yields sharper spectra than STFT, stable τ-band trajectories, and species-specific multi-scale “signatures.” Coupled with spike statistics and a lightweight ML pipeline, we obtain reproducible diagnostics under leave-one-file-out validation. All analyses are timestamped, audited, and designed for low-RAM devices.