论文标题
正弦频率估计通过梯度下降
Sinusoidal Frequency Estimation by Gradient Descent
论文作者
论文摘要
正弦参数估计是从光谱分析到时间序列预测的应用中的一项基本任务。然而，由于误差函数是非凸，并且与局部最小值密集填充，因此通常不可能通过梯度下降估算正弦频率参数。因此，不断增长的可区分信号处理方法的家族无法调整振荡组件的频率，从而阻止了它们在广泛的应用中的使用。这项工作提出了一种使用复杂指数替代物和任何基于一阶梯度的优化器的连线衍生物进行联合正弦频率和振幅估计的技术，从而使神经网络控制器的最终终端训练无约束，从而实现了无约束的正弦模型的终端训练。
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.
