A Unified Filtered Operator Approach for Noise-Resistant Analysis of Mass Spectrometry Data: Case Study on Opiates (Replicate 2, 90V)

We present a novel mathematical framework—the unified filtered operator—for the noise-resistant and context-aware analysis of time-of-flight mass spectrometry (TOF-MS) data. Unlike classical calculus, which is susceptible to noise and artifacts in all regions of the signal, the unified operator applies differentiation only within experimentally validated or physically meaningful (filtered) regions. Using real TOF-MS data for opiates (Replicate 2, 90V), we demonstrate that our method effectively suppresses irrelevant fluctuations and enhances the interpretability of spectral data. The results support the unified operator as a robust tool for modern analytical chemistry and signal processing.The author acknowledges the use of OpenAI’s language model for assistance in drafting certain sections of this worklNote on Figure 1:<br>Due to a rendering issue in the exported PDF, the graphical representation of Figure 1 may appear partially missing or distorted. The complete figure, including both the classical derivative and the unified filtered operator spectrum, is available as a supplementary image file and was verified during the numerical analysis stage.