The Effectiveness of the Piecewise Monotonic Approximation Method for the Peak Estimation of Noisy Univariate Spectra

We present examples of peak estimation to measurements of Raman, Infrared and NMR spectra by the piecewise monotonic data approximation method. The structural differences of these spectra, the complexity of the underlying physical laws and the error included in the measurements make this a good test of the effectiveness of the method. Precisely, if a number of monotonic sections of the data is required, then the optimal turning points and the least sum of squares of residuals are computed in quadratic complexity with respect to the number of data. This is a remarkable result because the problem may require an enormous number of combinations in order to find the optimal turning point positions. Our results exhibit some strengths and indicate certain advantages of the method. Therefore, they may be helpful to the development of new algorithms that are particularly suitable for peak estimation in spectroscopy calculations.