Abstract
We propose in this work the use of Dilation theory for non-stationary signals and their time/Doppler spectra to embed the underlying spectral measure on the Special Unitary group SU(n). The Dilation theory gives access to rotation-like matrices built in with partial correlation coefficients. Due to the non-stationary condition, the time/Doppler spectra is associated with a path on SU(n). We use next the Square root Velocity Transform which has been proven to be equivalent to a first order Sobolev metric on the space of shapes. Because the metric in the space of curves naturally extends to the space of shapes, this enables a comparison between curves’ shapes and allows then the classification of time/Doppler spectra.
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Bouleux, G., Barbaresco, F. (2019). Dilation Operator Approach and Square Root Velocity Transform for Time/Doppler Spectra Characterization on SU(n). In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2019. Lecture Notes in Computer Science(), vol 11712. Springer, Cham. https://doi.org/10.1007/978-3-030-26980-7_4
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