8 February 2007 The homogeneous dispersive lineshape as a wavelet basis
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The frequency domain susceptibility of all materials results from the collective response of absorptive resonances. The concomitant dispersive response follows according to the Kramers-Kronig relations for causal transfer functions. For an inhomogeneously broadened spectrum that comprises a collection of frequency-shifted homogeneously broadened absorption lines, analysis of the response is in principle straightforward and repetitive. The prospect that these regular resonant features might serve as a mathematical basis for constructing an arbitrary spectral susceptibility suggests the use of their mathematical lineshape as a mother wavelet in a wavelet basis.
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Alan E. Craig, Alan E. Craig, } "The homogeneous dispersive lineshape as a wavelet basis", Proc. SPIE 6482, Advanced Optical and Quantum Memories and Computing IV, 648203 (8 February 2007); doi: 10.1117/12.716385; https://doi.org/10.1117/12.716385

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