Papers › Sinusoidal Frequency Estimation by Gradient Descent

Sinusoidal Frequency Estimation by Gradient Descent

26 Oct 2022arXiv:2210.14476archive 2025-07-28

Ben Hayes, Charalampos Saitis, György Fazekas

Sinusoidal parameter estimation is a fundamental task in applications from spectral analysis to time-series forecasting. Estimating the sinusoidal frequency parameter by gradient descent is, however, often impossible as the error function is non-convex and densely populated with local minima. The growing family of differentiable signal processing methods has therefore been unable to tune the frequency of oscillatory components, preventing their use in a broad range of applications. This work presents a technique for joint sinusoidal frequency and amplitude estimation using the Wirtinger derivatives of a complex exponential surrogate and any first order gradient-based optimizer, enabling end to-end training of neural network controllers for unconstrained sinusoidal models.

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