Hilbert transform: Applications to atomic spectra

Abstract

Publisher's copyright statement:Reprinted with permission from the American Physical Society: Whittaker, K. A. and Keveaney, J. and Hughes, I. G. and Adams, C. S. (2015) 'Hilbert transform : applications to atomic spectra.', Physical review A., 91 (3). 032513 c 2015 by the American Physical Society. Readers may view, browse, and/or download material for temporary copying purposes only, provided these uses are for noncommercial personal purposes. Except as provided by law, this material may not be further reproduced, distributed, transmitted, modi ed, adapted, performed, displayed, published, or sold in whole or part, without prior written permission from the American Physical Society. Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. In many areas of physics, the Kramers-Kronig relations are used to extract information about the real part of the optical response of a medium from its imaginary counterpart. In this paper we discuss an alternative but mathematically equivalent approach based on the Hilbert transform. We apply the Hilbert transform to transmission spectra to find the group and refractive indices of a Cs vapor and thereby demonstrate how the Hilbert transform allows indirect measurement of the refractive index, group index, and group delay while avoiding the use of complicated experimental setups.

Quantum cascade laser-based reflectance spectroscopy: a robust approach for the classification of plastic type

“…This spectrum was then converted to its imaginary analytic signal using the Hilbert transform function in MATLAB (R2018a). The Hilbert transform was utilized as an alternative to the Kramers-Kronig [20]. The resulting spectrum was smoothed (moving average of 150) and then the 1697-1550 cm −1 region was removed from each spectrum due to a lack of identifying spectral features for plastics in this region.…”

An introduction to fractional calculus

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