Optimization method for variable fractional delay filters based on gradient descent

In order to address the requirements for low distortion transmission of variable fractional delay filters, an optimization method based on gradient descent and root mean square propagation was proposed. Firstly, the matrix form of the objective function and gradient expressions were derived, and an exponential moving average was used to adjust the step size based on historical and current gradient information. Secondly, the weight update mechanism incorporated the residual covariance matrix from previous iterations, thereby enhancing the approximation between the frequency response of the filter and the ideal response. Finally, comparisons with existing methods were conducted on the aspects of complexity and error. Simulation results demonstrate that, compared with the traditional weighted least square method, the proposed method effectively reduces the normalized root mean square error by 34.36% while maintaining high accuracy in both local amplitude and group delay.