Translation-Invariant Zero-Phase Wavelet Methods for Feature Extraction in Terahertz Time-Domain Spectroscopy

Area of Science:

• * Computational Signal Processing
• * Spectroscopic Analysis
• * Terahertz (THz) Science

Background:

• * Wavelet transforms are crucial for processing terahertz time-domain spectroscopy (THz-TDS) data.
• * Previous THz-TDS studies have not explored the impact of different wavelet transform types.
• * Understanding these differences is key for accurate spectral feature extraction.

Purpose of the Study:

• * To investigate and compare the implications of using Maximal Overlap Discrete Wavelet Transform (MODWT) versus Discrete Wavelet Transform (DWT) in THz-TDS.
• * To analyze the translation-invariance properties and phase-shift effects of both DWT and MODWT.
• * To guide researchers in selecting the optimal wavelet analysis tool for THz spectroscopy applications.

Main Methods:

• * Analytical comparison of DWT and MODWT, focusing on translation-invariance and phase characteristics.
• * Experimental validation using reflection THz-TDS measurements of α-lactose monohydrate.
• * Multiresolution analysis (MRA) to examine detail coefficients from both wavelet transforms.

Main Results:

• * Discrete Wavelet Transform (DWT) yields spectroscopic features that vary with overlapping frequency ranges.
• * Maximal Overlap Discrete Wavelet Transform (MODWT) provides consistent features irrespective of the spectral range due to its translation-invariance.
• * MODWT detail coefficients are associated with zero-phase filters, while DWT coefficients exhibit misalignments from down/up-sampling, impacting absorption line localization.

Conclusions:

• * MODWT is advantageous for THz-TDS due to its translation-invariance and zero-phase filtering properties, ensuring accurate spectral feature representation.
• * DWT's inherent misalignments can adversely affect the precise localization of spectral features in THz-TDS.
• * This study provides critical insights for selecting appropriate wavelet analysis methods in THz spectroscopy.