B-spline wavelet transform in voltammetry

In WT computation, many wavelet functions have been proposed by different workers. The simplest one, the Harr wavelet - which is also the first member of the family of Daubechies wavelets [7] - has been known for more 

In voltammetry, the spline wavelet was chosen as the major wavelet function for data de-noising. The function has been applied successfully to analyse voltammetric data since 1994 by Lu and Mo [9]. Mo and his co-workers have published more than fifteen papers on this topic in various journals. The spline wavelet is different from the Daubechies wavelet functions. Mathematically, the mth order basis spline (B-spline) wavelet, Nm, is defined recursively by convolution of the Harr wavelet function as follows [10]  

The symbol denotes the convolution operation between Nm-i and Nm - The kth term of Nm is given by 

In spline wavelet computation, optimization needs to be carried out on two parameters, namely the order of B-spline, m, and the truncation frequency or frequency scale, L, which represents the cut-off (or truncation) frequency value between the useful signal and noise. Details of the B-spline theory can be found in the references [12,13]. 

Reproduced from reference [14] with kind permission of Science in China Press. 

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