Improved Identification of Noisy Spectra Using Higher-Ordered Correlation Spectral Analysis

Abstract

We used a higher-order correlation-based method of comparison for spectral identification. Higher-order correlations are an extension of the more familiar second-order cross-correlation function and have the significant advantage of being theoretically shown to eliminate noise of unknown spectral density under certain conditions. Specifically, we applied a third-order correlation technique to the identification of similar IR spectra in the presence of noise. We were able to reduce the effects of noise from a second-order correlation measurement by further processing the measurement with a third-order autocorrelation. Our results showed that the third-order correlation-based method increased the probability of detection of a spectrum in the presence of noise, when compared to using a second-order technique alone. The probability of detection increased enough at low signal-to-noise ratios that this technique may be useful when a second-order correlation technique is not acceptable. The third-order technique is applicable to a single experiment, but improved results were found by averaging the results of multiple experiments.