The fan-chirp transform for non-stationary harmonic signals

This paper presents a novel transform related to the framework of warping operators when the continuous time warping mapping is a second-order polynomial. This case is proven in the paper to be the only one from the aforementioned group that marginalizes the Wigner distribution along line paths, in particular, with a fan geometry. The properties and attributes of the fan-chirp transform (FChT) along with the analytical characterization of harmonically related Gaussian chirplets bear especial relevance in the paper. This analysis shows that for chirp-periodic signals the FChT can reach the limit of the time–frequency (TF) uncertainty principle, while simultaneously keeping the cross-terms at minimum level. The formulation of the fast digital computation of the FChT is also provided in the paper. Two practical scenarios—the analysis of speech with natural intonation and bat ultrasound—validate the theoretical developments and shows manifestly the eloquent competitive performance of the new transform.