Spectral estimation in highly transient data

We propose a new framework for estimating different frequencies in piece-wise periodic signals with time varying amplitude and phase. Through a 3-dimensional delay embedding of the introduced model, we construct a union of intersecting planes where each plane corresponds to one frequency. The equations of each of these planes only depend on the associated frequency, and are used to calculate the tone in each segment. A sparse subspace clustering technique is utilized to find the segmentation of the data, and the points in each cluster are used to compute the normal vectors. In the presence of white Gaussian noise, principal component analysis is used to robustly perform this computation. Experimental results demonstrate the effectiveness of the proposed framework.