Translation-Invariant Zero-Phase Wavelet Methods for Feature Extraction in Terahertz Time-Domain Spectroscopy
Wavelet transform is an important tool in the computational signal processing of terahertz time-domain spectroscopy (THz-TDS) measurements. Despite its prevalence, the effects of using different forms of wavelet transforms in THz-TDS studies have not been investigated. In this paper, we explore the...
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MDPI AG
2022-03-01
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| Series: | Sensors |
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| Online Access: | https://www.mdpi.com/1424-8220/22/6/2305 |
| _version_ | 1797442307872522240 |
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| author | Mahmoud E. Khani Mohammad Hassan Arbab |
| author_facet | Mahmoud E. Khani Mohammad Hassan Arbab |
| author_sort | Mahmoud E. Khani |
| collection | DOAJ |
| description | Wavelet transform is an important tool in the computational signal processing of terahertz time-domain spectroscopy (THz-TDS) measurements. Despite its prevalence, the effects of using different forms of wavelet transforms in THz-TDS studies have not been investigated. In this paper, we explore the implications of using the maximal overlap discrete wavelet transform (MODWT) versus the well-known discrete wavelet transform (DWT). We demonstrate that the spectroscopic features extracted using DWT can vary over different overlapping frequency ranges. On the contrary, MODWT is translation-invariant and results in identical features, regardless of the spectral range used for its implementation.We also demonstrate that the details coefficients obtained by the multiresolution analysis (MRA) using MODWT are associated with zero-phase filters. In contrast, DWT details coefficients suffer from misalignments originated from the down- and upsampling operations in DWT pyramid algorithm. Such misalignments have adverse effects when it is critical to retain the exact location of the absorption lines. We study the differences of DWT and MODWT both analytically and experimentally, using reflection THz-TDS measurements of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>-lactose monohydrate. This manuscript can guide the researchers to select the right wavelet analysis tool for their specific application of the THz spectroscopy. |
| first_indexed | 2024-03-09T12:39:57Z |
| format | Article |
| id | doaj.art-80b2ba19f3e0438a8dc41b28c29848bd |
| institution | Directory Open Access Journal |
| issn | 1424-8220 |
| language | English |
| last_indexed | 2024-03-09T12:39:57Z |
| publishDate | 2022-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Sensors |
| spelling | doaj.art-80b2ba19f3e0438a8dc41b28c29848bd2023-11-30T22:19:05ZengMDPI AGSensors1424-82202022-03-01226230510.3390/s22062305Translation-Invariant Zero-Phase Wavelet Methods for Feature Extraction in Terahertz Time-Domain SpectroscopyMahmoud E. Khani0Mohammad Hassan Arbab1Biomedical Engineering Department, Stony Brook University, Stony Brook, NY 11790, USABiomedical Engineering Department, Stony Brook University, Stony Brook, NY 11790, USAWavelet transform is an important tool in the computational signal processing of terahertz time-domain spectroscopy (THz-TDS) measurements. Despite its prevalence, the effects of using different forms of wavelet transforms in THz-TDS studies have not been investigated. In this paper, we explore the implications of using the maximal overlap discrete wavelet transform (MODWT) versus the well-known discrete wavelet transform (DWT). We demonstrate that the spectroscopic features extracted using DWT can vary over different overlapping frequency ranges. On the contrary, MODWT is translation-invariant and results in identical features, regardless of the spectral range used for its implementation.We also demonstrate that the details coefficients obtained by the multiresolution analysis (MRA) using MODWT are associated with zero-phase filters. In contrast, DWT details coefficients suffer from misalignments originated from the down- and upsampling operations in DWT pyramid algorithm. Such misalignments have adverse effects when it is critical to retain the exact location of the absorption lines. We study the differences of DWT and MODWT both analytically and experimentally, using reflection THz-TDS measurements of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>-lactose monohydrate. This manuscript can guide the researchers to select the right wavelet analysis tool for their specific application of the THz spectroscopy.https://www.mdpi.com/1424-8220/22/6/2305maximal overlap discrete wavelet transformterahertz time-domain spectroscopyfeature extractionmaterial characterization |
| spellingShingle | Mahmoud E. Khani Mohammad Hassan Arbab Translation-Invariant Zero-Phase Wavelet Methods for Feature Extraction in Terahertz Time-Domain Spectroscopy Sensors maximal overlap discrete wavelet transform terahertz time-domain spectroscopy feature extraction material characterization |
| title | Translation-Invariant Zero-Phase Wavelet Methods for Feature Extraction in Terahertz Time-Domain Spectroscopy |
| title_full | Translation-Invariant Zero-Phase Wavelet Methods for Feature Extraction in Terahertz Time-Domain Spectroscopy |
| title_fullStr | Translation-Invariant Zero-Phase Wavelet Methods for Feature Extraction in Terahertz Time-Domain Spectroscopy |
| title_full_unstemmed | Translation-Invariant Zero-Phase Wavelet Methods for Feature Extraction in Terahertz Time-Domain Spectroscopy |
| title_short | Translation-Invariant Zero-Phase Wavelet Methods for Feature Extraction in Terahertz Time-Domain Spectroscopy |
| title_sort | translation invariant zero phase wavelet methods for feature extraction in terahertz time domain spectroscopy |
| topic | maximal overlap discrete wavelet transform terahertz time-domain spectroscopy feature extraction material characterization |
| url | https://www.mdpi.com/1424-8220/22/6/2305 |
| work_keys_str_mv | AT mahmoudekhani translationinvariantzerophasewaveletmethodsforfeatureextractioninterahertztimedomainspectroscopy AT mohammadhassanarbab translationinvariantzerophasewaveletmethodsforfeatureextractioninterahertztimedomainspectroscopy |