We describe the application of the discrete wavelet transform (DWT) in extracting the characteristic absorption signatures of materials from terahertz reflection spectra. We compare the performance of different mother wavelets, including Daubechies, least asymmetric (LA), and Coiflet, based on their phase and gain functions and filter lengths. We show that the phase functions of the wavelet and scaling filters result in spectral shifts to the absorption lines in the wavelet domain. We provide a solution by calculating advancement coefficients necessary to achieve effective zero-phase-function DWT. We demonstrate the utility of this signal processing technique using $\alpha$-lactose monohydrate/polyethylene samples with different levels of rough surface scattering. In all cases, the DWT-based algorithm successfully extracts resonant signatures at 0.53 and 1.38 THz, even when they are obscured by the rough surface scattering effects. The DWT analysis with accompanying phase corrections can be utilized as a robust technique for material identification in nondestructive evaluation using terahertz spectroscopy.

中文翻译：

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相位函数对使用离散小波变换识别太赫兹光谱特征的影响

我们描述了离散小波变换 (DWT) 在从太赫兹反射光谱中提取材料的特征吸收特征中的应用。我们比较了不同母小波的性能，包括 Daubechies、最小不对称 (LA) 和 Coiflet，基于它们的相位和增益函数以及滤波器长度。我们表明小波和缩放滤波器的相位函数导致小波域中吸收线的光谱偏移。我们通过计算实现有效零相位函数 DWT 所需的推进系数来提供解决方案。我们使用具有不同粗糙表面散射水平的 $\alpha$-乳糖一水合物/聚乙烯样品证明了这种信号处理技术的实用性。在所有情况下，基于 DWT 的算法都成功地提取了 0 处的共振特征。53 和 1.38 THz，即使它们被粗糙的表面散射效应所掩盖。带有相位校正的 DWT 分析可用作使用太赫兹光谱进行无损评估中的材料识别的强大技术。