Wavelet transform applications in analytical chemistry

Abstract

The wavelet transform has been established with the Fourier transform as a data-processing method in analytical chemistry. The main fields of application in analytical chemistry are related to denoising, compression, variable reduction, and signal suppression. Analytical applications were selected showing prospects and limitations of the wavelet transform. An important aspect consists in showing the advantage of wavelet transform over Fourier transform with respect to dual localization of a signal in both the original and the transformed domain enabling principal new application fields in comparison with Fourier transform.

Application of FTIR Spectroscopy to Agricultural Soils Analysis

“…Although wavelet decomposition by itself does not produce a compressed representation of the original data, data reduction can be achieved by eliminating the wavelet coefficients that do not contain valuable information. Various approaches have been reported in the literature for selecting the most relevant coefficients, such as eliminating all "small" coefficients using for instance either thresholding (Kai-man Leung et al 1998;Ehrentreich 2002), entropy (Kai-man Leung et al 1998), mutual information (Alsberg et al 1998), maximum likelihood (Leger&Wentzell 2004), or genetic algorithms (Depczynski et al 1999), or retaining only the coefficients with the highest variance (Trygg&Wold 1998) as depicted in Figure 6. Once data compression has been achieved, the remaining coefficients can be used as input variables for a neural network that creates a non-linear mapping between these inputs and the property (or properties) of interest.…”

Simultaneous Spectrophotometric Determination of Metformin Hydrochloride and Glibenclamide in Binary Mixtures Using Combined Discrete and Continuous Wavelet Transforms

“…13,14 Wavelet transform is a strong tool for signal de-noising 15 and baseline removal, 16 signal compression and processing, and multicomponent analysis; it has been established as a powerful technique in analytical chemistry. [17][18][19][20] By means of wavelet transform, an original signal can be decomposed into localized contributions characterized by a scale parameter. Each contribution represents a portion of the signal with a different frequency.…”

Implementation of the Discrete Wavelet Transform Used in the Calibration of the Enzymatic Biosensors

“…Evaluation of cholinesterase activity is the crucial factor in the construction of biosensors, however, in the case of multicomponent samples (more common in reality) is absolutely essential include appropriate data processing tools to find relationships between the biosensor responses and the measured data. In most cases, it is necessary a first data pretreatment step in order to explore and validate these obtained information (Ehrentreich, 2002). Many applications related with the use of biosensor responses entail data interpretation problem related to: (1) noisy records due to temperature changes; (2) data acquisition noise present in records, (3) presence of interference signals in the biosensor response mainly contaminated by signals coming for the electrochemical equipment i.e.…”