For the analysis of spectroscopic data, model fitting approaches are commonly applied. The spectrum model applied in these fitting processes significantly influences the performance of the spectroscopic evaluation, which can be critical in real-time process diagnostics and control. In this work a spectrum model is introduced that uses a polynomial description of absorbances, transmittances, or similar in dependence on parameters such as temperature, pressure, and mole fraction. Using this approach, either experimental spectra or spectrum databases can be compressed into a matrix of polynomial coefficients. The evaluation of this model consists of a single matrix multiplication and, with a slight modification, derivatives with regard to specific parameters can be calculated in the same way. Both these points are important to model fitting methods for spectroscopic data, as the simple evaluation method allows for a fast analysis and the direct calculation of derivatives simplifies the application of gradient-based fitting methods. Additionally, the easy parallelizability of the matrix multiplication promotes the application of this method in real-time evaluations on programmable logic devices.