Novel algorithms for wavelet computation in IR spectroscopy

WT has been proposed as a new method for compressing spectra for storage and library searching in our study. In this kind of work, spectra are reconstructed from time to time from the compressed data. In order to maintain the quality of the reconstructed spectra, we have introduced another technique called the translation-rotation transformation (TRT) method [23] in the wavelet computation. In the FWT operation, the spectral data vector Cj needs to be extended periodically at the two extremes in the following manner  

In the real situation, or in practice, the first data point, cj.i, and the last data point, cj n, at the two extremes do not have a common value. As a result, a small delay which results from discontinuity of the spectral data at the boundary will be observed at both ends of the reconstructed spectrum. Such a phenomenon is known as the side-lobe problem and causes deterioration of the quality of the reconstructed data (Fig. 3) [24]. The TRT algorithm 

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