ANALYSIS OF FLOW-INJECTION PEAKS WITH ORTHOGONAL POLYNOMIALS

Digitized transient signals such as those acquired in flow injection analysis may be decomposed by a generalized Fourier expansion into a weighted linear combination of discrete orthogonal polynomials. Together, the coefficients from such an expansion form a spectrum analogous to that of the magnitude spectrum of a discrete Fourier transform and provide a useful alternative means of signal identification. This flexible method of representing peak shapes in flow injection (and elsewhere) is not reliant upon any single mathematical model. Two families of functions, the Gram and Laguerre polynomials, were investigated. Both series were found to be sensitive to changes in peak shape and able to represent important features of flow injection time domains signals. Indeed, a small number of coefficients was sufficient to accurately approximate even highly bifurcated peaks. The Laguerre spectrum has a characteristic profile similar to that of the actual peak while the Gram spectrum typically has the characteristics of an ac transient signal. The Laguerre spectrum is more computationally expensive to produce since it requires optimization of a time scale parameter; a method for this is described. The utility and robustness of these representations are evaluated on real and simulated data. About 20-25 Gram coefficients and 7-10 Laguerre coefficients were found to provide a near-optimal balance between the ability to discriminate between various peak-shaped signals and robustness to noise. Abnormal peak shapes are readily identified.