Analysis of Complex Spectra Using Fourier Filtering

We present a method to analyze complex spectral data, such as that obtained from vibrational sum-frequency generation (SFG), using Fourier filtering. The proposed filter locates the center frequency of all resonances in a complex data set. The analysis is useful for spectral data that consist of multiple overlapping peaks or with sharp resonances that interfere with a broad background, in which locating resonances is of high interest to characterize spectra, but usually difficult to implement. We apply the filter to complex spectra obtained from maximum entropy analysis of both numerically generated SFG intensity data containing multiple resonances from known line-shape parameters and experimental SFG intensity data from the quartz/OTS/water interface. By having an unambiguous determination of the resonance frequencies, spectral analysis can be improved. The method also provides an easy check for validating interferometric measurements. Although the method is here applied to SFG data, it can be used with any type of complex spectral data (such as CARS) and is useful to eliminate the effects of a large nonresonant background.