Application of Dual‐Tree Complex Wavelet Transform for Spectra Background Reduction

This article presents a unique background‐cutting method for experimental data processing using the dual‐tree complex wavelet transform (DTCWT) algorithm. The presented technique is based on discrete wavelet theory (DWT) and overcomes numerous obstacles encountered in information retrieval that are present in commonly employed numerical techniques, especially fitting or filtering. The DTCWT also outperforms methods based on the Fourier transform. This method is universal, which allows the analysis of an arbitrarily selected data range and its position in time. Furthermore, it suits the special requirements of signal analysis and optimization, both preservation and bias reduction. This article discusses the implementation of an algorithm for background reduction, leading to the extraction and enhancement of the valuable information from spectra. The capabilities of wavelets for spectra data processing are demonstrated based on the example of significantly different spectra, namely, X‐ray powder diffraction and photoluminescence, measured for the crystal Ga 2 O 3 . Issues typical of the DWT application and important for robust and reliable data processing, such as the choice of wavelet family and the number of decomposition levels, are also discussed. It is available as a software package for background reduction.