Tamás L. Pap – Attila Khirer
Institute of Analytical Chemistry, University of Veszprém,
P.O.Box 158, H-8201 Veszprém, Hungary
Key words: chemometrics, Fourier transformation, potentiometry.
Fourier transformation is a data-manipulating tool for signal processing in analytical chemistry, of course, in potentiometry too. The processing of analytical signals on the basis of their Fourier transforms has an important role since the algorithm of the fast Fourier transformation was published. The Fourier transform is a reversible operation. Reversibility of the transformation operation is, however, essential if any advantage is to be realized by Fourier domain manipulations. In this work some useful manipulations were elaborated for potentiometry:
- Convolution. The convolution theorem of Fourier transformation states that the Fourier transform of the product of two functions is equivalent to the convolution of the Fourier transforms of the individual functions. In general, this theorem predicts that by multiplication with an appropriate weighting function in the Fourier domain, a data array can be convoluted with almost any desired function. For example in the case using cross-correlation technique.
- Interpolation. This method, e.g. zero filling in frequency domain, generates new data points between the original ones in the analytical signal.
- Smoothing. The signal has a different spatial frequency content from the noise, and this method is to zero those spatial frequencies arising from noise prior to reverse transformation.
- Baseline correction. This manipulation eliminates the low frequency information in Fourier domain.
- Differentiation and integration. The multiplication in the Fourier domain by (i2pf) is equivalent to differentiation, and the division by (i2pf) is equivalent to integration.
- Curve fitting of analytical signal in frequency domain.
- Storage of signals by using Fourier transform set free memory in the computer and makes possible the quick search and restore of signals.
The above listed manipulations have been successful used in potentiometry. The results are presented in this presentation.