Simplification of Complex EPR Spectra by Cepstral Analysis

As the Fourier transform of time-series data is known as the spectrum, the Fourier transform of the logarithm of the time-series data is called the cepstrum of the data. When cepstral analysis is applied to free induction decay signals of free radicals showing first-order EPR spectra, the identification of nuclear hyperfine coupling constants becomes simple. In a systematic manner, we have examined how the technique of cepstral analysis is affected by the presence of aliasing, noise, uncertainty in the time origin of the free induction decay, the presence of second-order hyperfine couplings, and the applications of various apodization methods. This technique was then applied to analyze the EPR spectrum of anthraquinone anion radical, and anion radicals of porphycene and tetrapropyl-porphycene, and the hyperfine coupling constants thus obtained were compared with published data. A good agreement was always found. We make a case for the usefulness of cepstral analysis in determining the hyperfine coupling constants of complex EPR spectra of organic free radicals.