The fan-chirp transform for non-stationary harmonic signals

Authors:
Luis Weruaga;Márian Képesi
Affiliations:
Commission for Scientific Visualisation, Austrian Academy of Sciences, Donau-City Strasse 1, 1220 Vienna, Austria;Signal Processing and Speech Communication Laboratory, Technical University of Graz, Inffeldgasse 12, 8010 Graz, Austria
Venue:
Signal Processing
Year:
2007

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Abstract

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.