Engine sounds are modeled as harmonic oscillations. Fourier series, sinusoidal components at integer multiples of the fundamental firing frequency. The harmonic-plus-noise framework decomposes the sound into deterministic harmonics and stochastic residual. This works well enough for steady-state operation but struggles with transient events — gear shifts, throttle changes, misfires — because the model assumes continuous oscillation, and transients are discontinuities.
Kim, Lee, and Park (arXiv:2603.09391, March 2026) observe that engine sounds are not sustained oscillations. They are sequential pressure pulses — each cylinder fires, releases a burst of exhaust gas, and falls silent until the next firing. The sound is a train of discrete impulses, not a continuous wave. Treating it as harmonic oscillation is a modeling convenience that discards the impulse structure.
The alternative: model each exhaust pulse individually, then route the pulse train through a Karplus-Strong resonator — the algorithm originally designed to synthesize plucked string sounds. A plucked string also produces a discrete impulse (the pluck) that excites a resonant body. The exhaust valve opens (pluck), the resonant structure of the exhaust manifold and tailpipe shapes the sound (string body). The analogy is physical, not metaphorical.
The result: 21% better harmonic reconstruction than harmonic-plus-noise models. The improvement is largest during transients, where the pulse model correctly captures the discontinuous firing events that the harmonic model smooths over.
The structural lesson is that the correct decomposition of a signal is not always into frequency components. Engine sound decomposes naturally into temporal events — individual firings — not into spectral harmonics. The harmonic decomposition works in steady state because a periodic pulse train has a Fourier series that matches the harmonic model. But the Fourier description is derived from the pulse structure, not the other way around. When the pulse structure changes (transients), the Fourier description fails because it was always the wrong primitive. The right atom of engine sound is the exhaust event, not the sine wave.