Sinusoidal Frequency Estimation by Gradient Descent

TL;DR

This paper introduces a novel gradient descent-based method for joint sinusoidal frequency and amplitude estimation, overcoming non-convexity issues and enabling end-to-end neural network training for oscillatory signal models.

Contribution

It presents a new technique using Wirtinger derivatives for efficient joint parameter estimation, expanding the applicability of differentiable signal processing methods.

Findings

Enables end-to-end training of neural controllers for sinusoidal signals.

Overcomes local minima issues in frequency estimation.

Improves accuracy of sinusoidal parameter estimation.

Abstract

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.