Fast and Accurate Generalized Harmonic Analysis Using Newton's Method

A fast and accurate method for Generalized Harmonic Analysis (GHA) is proposed. The proposed method estimates the parameters of a sinusoid and subtracts it from a target signal one by one. The frequency of the sinusoid is estimated around a peak of Fourier spectrum using Newton’s method, which is much faster than search methods. The amplitude and the phase are estimated to minimize the squared sum of the residue after extraction of estimated sinusoids from the target signal. A method to improve the accuracy of sinudoidal parameters using multi-dimensional Newton’s method is also proposed. This method is applied to the extracted sinusoidal parameters and minimizes the partial derivative vector of the squared error. Audio signals are analyzed by the proposed methods, which confirms the accuracy compared to the previous method.