We present a detailed description of the numerical implementation (for either MATLAB or GNU Octave) of a novel method for processing data with serial localized peaks intended to distinguish between individual components even when they form a mono-modal but complicatedly shaped structure [E.B. Postnikov et al. Mathematics 9 (2021) 2802]. The essence of the method consists of a cascade of local non-linear approximations by the Gaussian function at the vicinity of the zero-crossings for the signal’s Hilbert transform. At the first level, this procedure is applied to the processed signal directly; at the next level, it is applied to residuals between the signal and approximations on the previous levels. As a practical example, we consider the decomposition of Raman spectra recorded from different strains of Mycobacterium tuberculosis. Finally, we discuss other areas of applicability for the proposed method of signal processing.