Mathematical Tools in SpectraLab 


SpectraLab contains various tools for pre-processing and analyzing spectral and kinetic data. Most of these tools are available through the "Math" and "Analysis" sections of the Main Menu.
The "Math" section includes  simple mathematical operations on the traces (summarizing, multiplying, etc.). Some of these operations, such as taking the logarithm, exponentiation, and some other mathematical functions, are not available in the Menu but may be invoked through the Command Line (see their descriptions in the Glossary of SpectraLab Scripts). Additional, more advanced pre-processing tools available through Main Menu and/or through the Command Line are:
  • Re-sampling the traces to the desired sub-range and regular interval at X-axis. If necessary, this re-sampling involves third-order polynomial interpolation between the points using the Aitken algorithm  as implemented by Mifsud.
  • Moving-window third-order polynomial smoothing using Savitzky–Golay algorithm (requires regular distribution of the points by X-axis). The window may vary from 3 to 21 points (in the case of a three-point window, the second-order polynomial is applied).
  • Filtering-out outliers with "Triad" smoothing using Tukey's moving median algorithm . The window may be varied from 3 to 7 points.
  • Calculation of the first and second order derivatives using the five-point central differences algorithm. These calculations require regular distribution of points. In the case of noisy data, it is advisable to use Savitsky-Golay smoothing before differentiation. In contrast to the previous three techniques available through the Main Menu, differentiation can be invoked only through the Command Line (see #DER1 and #DER2 words in the Glossary of SpectraLab scripts). -
The "Analysis" section provides tools for:
  • fitting spectra by combinations of spectral standards using the multi-dimensional linear least-squares algorithm (SURFIT procedure)
  • non-linear least square approximation of traces by a pre-defined set of mathematical functions commonly used in the analysis of (bio)chemical data (CURFIT procedure), and
  • analysis of a series of spectra with the Principal Component Analysis (PCA) technique (SPAN procedure).
These methods are described in detail in separate pages of this Help System.