An algorithm for detecting oscillatory behavior in discretized data: the damped-oscillator oscillator detector

We present a simple algorithm for detecting oscillatory behavior in discrete data. The data is used as an input driving force acting on a set of simulated damped oscillators. By monitoring the energy of the simulated oscillators, we can detect oscillatory behavior in data. In application to in vivo deep brain basal ganglia recordings, we found sharp peaks in the spectrum at 20 and 70 Hz. The algorithm is also compared to the conventional fast Fourier transform and circular statistics techniques using computer generated model data, and is found to be comparable to or better than fast Fourier transform in test cases. Circular statistics performed poorly in our tests.

💡 Research Summary

The paper introduces a novel method for detecting oscillatory components in discretized time‑series data by exploiting the dynamics of simulated damped harmonic oscillators. Instead of directly applying a Fourier transform to the raw signal, the authors treat the data points as an external driving force, F(t), applied to a set of virtual oscillators each characterized by a natural frequency ω₀ and a damping coefficient γ. The motion of each oscillator follows the second‑order differential equation

  d²x/dt² + 2γ dx/dt + ω₀² x = F(t).

During simulation the instantaneous mechanical energy

  E(t) = ½