Optimization of apodization functions in terahertz transient spectrometry

Area of Science:

• Spectroscopy
• Signal Processing
• Optimization Techniques

Background:

• Terahertz transient spectroscopy (THz-TDS) is a powerful tool for analyzing materials.
• Apodization windows are crucial for processing time-domain data in THz-TDS.
• Existing windows may not be optimal for complex or asymmetric sample waveforms.

Purpose of the Study:

• To propose a novel quadratic programming optimization procedure for designing asymmetric apodization windows.
• To tailor these windows specifically to the shape of recorded time-domain sample waveforms.
• To enhance the performance of data analysis in THz-TDS.

Main Methods:

• A quadratic programming optimization procedure was developed.
• Asymmetric apodization windows were designed based on sample waveform characteristics.
• The performance of the designed windows was compared against conventional windows (rectangular, triangular, Hamming) using artificially degraded waveforms.
• Gaussian functions were used as examples for window optimization, with a formulation generalizable to other basis functions.

Main Results:

• The proposed method successfully designed asymmetric apodization windows.
• The designed windows demonstrated improved performance in both time and frequency domains compared to conventional windows.
• The optimization procedure is flexible and can utilize various basis functions.

Conclusions:

• The quadratic programming approach offers a superior method for designing tailored apodization windows in THz-TDS.
• This technique enhances the accuracy and effectiveness of terahertz waveform analysis.
• The developed method provides a versatile tool for optimizing signal processing in spectroscopy.