Download (direct link):
Another combination technique was developed by Zheng et al. [75,76], who coupled the spline wavelet and the Riemann-Liouville transform (RLT) together to filter random noise and extraneous currents in voltammetric signals. They processed both simulated and experimental data. The results showed that signals of SNR = 0.8 can be filtered. The errors of the peak current were less than 5% and those of the peak potential were less than 1%.
WT has been proposed as an alternative tool to overcome the limitations of FFT in the analysis of electrochemical noise measurements (ENM) data by Aballe et al. , who applied both WT and FFT methods to study various different corrosion systems covering a wide range of ENM signals. Results demonstrated that WT is applicable to those systems in which the
an overview of the applications in chemistry
FFT technique works. However, in cases where FFT fails, WT can still provide valuable knowledge about the behavior of the system. Using WT, the different ENM components contributing to the original signal can be characterized. Each component is defined by a set of wavelet coefficients, which contain information about the timescale characteristic of the associated corrosion event.
In differential pulse voltammetry (DPV) quantitative analysis, it is very difficult to measure the peak height of a component in a sample with low concentration. Chen et al.  employed a new type of wavelet function known as DOG (the difference of Gaussians) to process DPV signals. In this study, they first transformed the DPV signal of a sample in high concentration to determine a scale parameter, and then transformed the signals of samples with low concentration with the predetermined scale parameter. The results showed that a new linear calibration curve can be obtained and the detection range can be extended in the low concentration side.
Using the edge detection property of WT, an application of WT to determine the endpoint in potentiometric titration was proposed by Wang et al. . In this work, the authors used a second-order differential spline function to process the titration curve, and used the discrete wavelet coefficients to determine the endpoint. Titration curves of HCl, AcOH, H3PO4, and H2C2O4 were studied by this method. It was found that the endpoint could be determined easily and accurately.
Fourier self-deconvolution is an effective means for resolving overlapping bands, but this method requires a mathematical model to yield the deconvolution and it is quite sensitive to noises in the unresolved bands. A WT-based Fourier deconvolution was proposed by Zhang et al. , who obtained a discrete approximation from WT of the original data and substituted it for the original data to be deconvolved and then used another discrete approximation as a lineshape function to yield the deconvolution. After that, they employed the B-spline wavelet, instead of the apodization function, to smooth the deconvolved data to enhance the signal-to-noise ratio (SNR). This method is not adversely affected by noises in the original data as in the Fourier self-deconvolution. The results of this study  indicated that resolution can be significantly enhanced, especially for signals with higher noise level. Furthermore, this method does not require a mathematical model to yield the deconvolution.
In order to resolve the overlapping voltammetric peaks that can be described bythesech2 (hyperbolic secant squared) function, a new method known as the flip shift subtraction method (FSSM) was proposed by Wu et al. . The method is built on the basis of finding the peak positions using the CWT with the Marr wavelet. To guarantee the accuracy of the
application of wavelet transform in chemistry
determined peak position, a technique known as the crossed iterative algorithm of continuous wavelet transform and original signal (CIACWTOS) is proposed to locate the refined peak positions. The calculated results of synthetic peaks and experimental signals both agreed well with the theoretical predictions. In the case of severe noise (SNR = 10), the peak positions can still be obtained under the appropriate dilation parameter. This work demonstrated that CWT is an efficient tool for finding the peak positions using the Marr wavelet even in the case of serious overlap and noise.
The online WT algorithm was adopted in Reference  for development of a WT-based voltammetric analyzer. Because the online WT decomposes the sampled signal simultaneously with the progress of sampling, the developed voltammetric analyzer gives all the components contained in the sampled voltammogram. Applications of the equipment in linear sweep voltammetric analysis of mixtures of Pb(II) and Tl(I) and in square-wave voltammetric analysis of mixture of Cd(II) and In(III) were investigated in this study . The results showed that the overlapping peaks of Pb(II) and Tl(I) can be separated easily, and the peak position after the online wavelet transform did not change. The linearity of the calibration curves for Cd(II) and In(III) in the overlapping square-wave voltammograms was retained after on-line WT. Quantitative determination of Cd(II) and In(III) in mixture samples were also investigated, with recovery rates between 92.5% and 107.1%.