Comparison of Detection Methods for Closely Spaced Spectral Lines: The Role of the Second Derivative and Noise Distortions

The aim of this study is a comparative analysis of methods for improving spectral resolution in the detection of closely spaced spectral lines under conditions of their partial overlap. The main focus is on the second derivative method, which enhances the contrast between components by emphasizing high-frequency features of the signal. In numerical modeling in the MATLAB environment, two approaches have been studied: direct detection of the total signal and analysis of its second derivative. Two identical Gaussian signals with a variable interpeak distance d supplemented by additive noise have been simulation. The results have shown that the second derivative method reduces the minimum visual resolution threshold from ddirect = 2.1 to dmod = 1.6, providing a 31% gain in resolving power. However, noise fluctuations (SNR = 40 dB) significantly distort the derivative signals, masking the troughs between peaks. Smoothing the data with a moving average partially suppresses the noise but leads to broadening of the peaks by 15%, demonstrating a compromise between accuracy and preservation of the signal shape.