GENERALIZED FOURIER SMOOTHING OF FLOW-INJECTION ANALYSIS DATA

The Fourier transform is widely used for smoothing data such as those from now injection analysis (FIA). The effectiveness of this method ca n be enhanced if, in addition to the standard complex exponential func tions, the Fourier transform is generalized to use other sets of compl ete, orthogonal functions such as the Gram or Meixner polynomials as i ts basis functions. The choice of which set of basis functions to use depends on its efficiency on a given peak. Using simulated noisy FIA p eaks differing in degree of skewness, it was found that the standard c omplex exponential set is best-suited for symmetric or nearly symmetri c peaks, and the Meixmer set, for moderate to greatly skewed peaks. Th e Gram set weakly favors skewed peaks, but it is not more effective th an both the complex exponential and Meixner sets over any portion of t he skewness range studied. The problem of determining the optimal spec tral cutoff point was cast in terms of hierarchical model selection, a nd a generalized Akaike information-theoretic criterion (GAIC) was eva luated for its ability to find the best filter order. Use of an effici ent basis minimizes the chance of selecting a nonoptimal filter order. The combination of generalized Fourier filtering and the GAIC provide s an attractive means to filter FIA data automatically.