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.