"The Analytic Stockwell Transform"Moukadem, AliThe Stockwell transform is a time-frequency transform which decomposes a finite energy signal on a family of elementary functions obtained through translating modulating and dilating an admissible window. As so, it constitutes a genuine hybridization of the short-time Fourier transform and of the continuous wavelet transform. The Stockwell transform performs a multiresolution analysis while keeping an absolutely referenced phase information. The present work proposes a so-called analytic Stockwell transform. To that aim, generalized Stockwell transforms in the time-frequency and time-scale planes are first constructed, relying on novel admissibility conditions for the analyzed window. The link between the generalized Stockwell transforms and the continuous wavelet transform is then leveraged to demonstrate analyticity in the time-scale plane. Furthermore, numerical experiments shows that the analytic Stockwell transform coincides, up to multiplication by a nonvanishing function, with the hyperbolic Gaussian analytic function. In particular, the statistics of the zeros of the analytic Stockwell transform perfectly fit the statistics of the zeros of the hyperbolic Gaussian Analytic Function. |
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