The Application in Processing Analytical Chemistry Signals of a Cardinal Spline Approach to Wavelets
- 1 August 1997
- journal article
- Published by American Chemical Society (ACS) in Analytical Chemistry
- Vol. 69 (15) , 3053-3057
- https://doi.org/10.1021/ac961145k
Abstract
The mth order B-spline Nm(x) with integer knots generates a multiresolution analysis, ···⊂V-1⊂V0⊂···, with the mth order of approximation in wavelet transformation (WT). We have compared the WT method with Fourier transformation processing analytical chemistry signals in detail and have found that the WT method has many advantages. This method can directly provide the frequency domain distribution of a signal in a time domain. The algorithms are simpler and take less time in operation, and one needs only to decompose the digital signal rather than to undertake many transformations. Moreover, it is not necessary to preprocess the original signal to analyze the pattern of data and to know the statistical character of the noise. When the signal-to-noise ratio is 0.2, the processed results of theoretical and experimental data can still be satisfactory.Keywords
This publication has 8 references indexed in Scilit:
- ChemometricsAnalytical Chemistry, 1994
- Properties and applications of the Fourier transform of a voltammetric waveJournal of Electroanalytical Chemistry, 1992
- The Fourier transform of a voltammetric peak and its use in resolution enhancementJournal of Electroanalytical Chemistry and Interfacial Electrochemistry, 1990
- The wavelet transform, time-frequency localization and signal analysisIEEE Transactions on Information Theory, 1990
- Multifrequency channel decompositions of images and wavelet modelsIEEE Transactions on Acoustics, Speech, and Signal Processing, 1989
- Approximation by smooth multivariate splinesTransactions of the American Mathematical Society, 1983
- Fluorescence line narrowing spectroscopy in organic glasses containing PPB levels of polycyclic aromatic hydrocarbonsAnalytical Chemistry, 1978
- Determination of subnanogram quantities of silver in snow by furnace atomic absorption spectrometryAnalytical Chemistry, 1973