Wavelet Analysis in Analytical Chemistry

Abstract

Wavelet analysis has been proved to be a high performance signal processing technique. In this paper, with a brief introduction of the basic theory and the Mallat pyramid algorithm of the wavelet analysis, new algorithms which are more suitable for processing analytical signals were described, and the works which we have done recently were reported. The main characteristic of the wavelet transform is the dual localization property in both time domain and frequency/scale domain, which enables the wavelet analysis to decompose a signal into contributions which represent the information of different frequency contained in the original signal. Therefore, many applications based on the frequency analysis can be achieved by the technique, such as de-noising, baseline correction, and resolution of overlapping signal, etc. Another characteristic of the wavelet analysis is that it is a linear decomposition, which enables us to do quantitative determination using the decomposed contributions.

Application of the wavelet transform method in quantitative analysis of Raman spectra

“…The wavelet transform (WT) method 3 has been shown to be a high-performance signal-processing technique, 4 and its performance for filtering noise from chemical signals has been investigated. 5,6 In 1996, Mittermayr et al 7 studied modulating Gaussian data with white noise and compared the results of several de-noising methods, and concluded that the WT method is more efficient than traditional methods such as Fourier filter and Savitzky-Golay filter.…”

Wavelets and related time‐frequency techniques in magnetic resonance spectroscopy

“…Two other algorithms for the quantification of FIDs have been proposed. The first one, due to Leclerc,[17][18][19] makes use of the bilinear Wigner-Ville distribution [eqn (7)] and its smoothened version [eqn (8)] with g(t) = (t) (PWV). The point is that the amplitude and the damping rate of a single damped, complex, sinusoid, supported on positive time, can be extracted from its PWV distribution, by linear regression on the logarithm of the latter.…”

“…For further information, we refer the reader to the many excellent reviews available in the literature, notably the contributions by Aldroubi and Unser, 1,3 or the textbooks of Daubechies 4 or Torrésani. 5 We may also point out the very recent reviews by Leung et al 6 and Shao and Cai, 7 where the whole field of wavelet applications in analytical chemistry is surveyed (but little on MRS, however).…”

Wavelet-based classification and influence matrix analysis method for the fast discrimination of Chinese herbal medicines according to the geographical origins with near infrared spectroscopy

“…10 The redundant information in the spectral data and information irrelevant to the response will worsen the quality of the model and the precision of the prediction. Various signal preprocessing techniques, including variable selection, 7 orthogonal signal correction (OSC), 11 uninformative variable elimination (UVE), 12 frequency-domain processing using wavelet transformation (WT), 13 have been employed to eliminate background and noise to improve the robustness and reliability of the model in both calibration and classi¯cation. WT has been proven to be a powerful tool for dimension reduction and noise removal.…”