Identifying non-linear fractional chirps using unsupervised Hilbert approach

Non-linear time-frequency structures, naturally present in large number of applications, are difficult to apprehend by means of Cohen´s class methods. In order to improve readability, it is possible to generate other class of time-frequency representations using time and/or frequency warping operators. Nevertheless, this requires the knowledge of a non-linear warping function which characterizes the time-frequency content. For this purpose, an unsupervised approach to estimate the warping function is proposed here in the case where time-frequency structures can be represented by chirps with a fractional order. To this end, a Hilbert transform-based technique is applied in order to robustify phases jumps detection. Since those phases jumps define the fractional order in a unique way, the chirp order can be estimated by a bisection method. Results obtained from synthetic data illustrate the attractive outlines of the proposed method.