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.