Chi-Squared-Based Filters for High-Fidelity Signal-to-Noise Ratio Enhancement of Spectra

Abstract

When reconstructing a measured spectrum to enhance its signal-to-noise ratio (SNR), the objective is to minimize the variance between the smooth reconstructed spectrum and the original measured spectrum, hence to attain an acceptably small χ2 value. The χ2 value thus measures the fidelity of the reconstruction to the original. Smoothness can be conceived as attenuated variation between adjacent points in a spectrum. Thus, a conceptual change in the application of the χ2 function to the difference between adjacent points of the reconstructed spectrum permits its use, in principle, as both a measure of smoothness and a measure of fidelity. We show here that implementations of this concept produce results superior to Savitzky–Golay filters.