Sound Matching with a Differentiable Karplus-Strong Algorithm
We present a self-supervised, event-based sound matching model using a differentiable extended Karplus-Strong algorithm. To avoid relying on external onset and fundamental frequency detectors, we explore training methodologies combining parameter losses on synthetic data with audio losses. We demonstrate that time-domain fractional delay interpolation provides gradient accuracy comparable to frequency-sampling while avoiding time-aliasing in highly resonant time-varying scenarios. Through systematic gradient analysis, we reveal that standard spectral losses provide no meaningful directional gradients for onset times, heavily degrading joint training. Training exclusively with parameter losses on synthetic data effectively learns fundamental frequency, timbral parameters, and onset times, but struggles to generalise to monophonic studio recordings of plucked guitar. External detectors combined with audio losses generalise best, isolating the model to timbre optimisation. While our Karplus-Strong decoder recovers interpretable parameters and naturally captures the transient characteristics of plucked guitar, Harmonics plus Noise baselines yield higher reconstruction fidelity by most metrics.