The homogeneous dispersive lineshape as a wavelet basis

摘要

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.