A Fourier series method for numerical Kramers-Kronig analysis

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Abstract
Using a time domain method the Kramers-Kronig integrals are derived without recourse to complex analysis (except in evaluating the Fourier transform of sgn (t)). From the time domain result, a Fourier series method for numerical evaluation of causality relations is derived. This method eliminates the need to use numerical integration, the use of logarithms in evaluating the function and the consideration of Cauchy principal parts. Through the use of the fast Fourier transform algorithm the calculation can be vary rapid. The accuracy of the technique is considered.

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