Chemical degradation of edible oils has been studied using conventional spectroscopic methods spanning the spectrum from ultraviolet to mid-IR. However, the possibility of morphological changes of oil molecules that can be detected at terahertz frequencies is beginning to receive some attention. Furthermore, the rapidly decreasing cost of this technology and its capability for convenient, in situ measurement of material properties, raises the possibility of monitoring oil during cooking and processing at production facilities, and more generally within the food industry. In this paper, we test the hypothesis that oil undergoes chemical and physical changes when heated above the smoke point, which can be detected in the 0.05–2 THz spectral range, measured using the conventional terahertz time-domain spectroscopy technique. The measurements demonstrate a null result in that there is no significant change in the spectra of terahertz optical parameters after heating above the smoke point for 5 min.

This paper presents an approach to classification of substances based on their terahertz spectra. We use geometric algebra to provide a concise mathematical means for attacking the classification problem in a coordinate-free form. For the first time, this allows us to perform classification independently of dispersion and, hence, independently of the transmission path length through the sample. Finally, we validate the approach with experimental data. In principle, the coordinate-free transformation can be extended to all types of pulsed signals, such as pulsed microwaves or even acoustic signals in the field of seismology. Our source code for classification based on geometric algebra is publicly available at: https://github.com/swuzhousl/Shengling-zhou/blob/geometricalgebra-classifier/GAclassifier/.

A generalized definition is presented of multipath angular spread, used to study the spatial correlation of the signal envelope in a three-dimensional wireless channel, both in the cases of a three-dimensional and a horizontal travel direction. Previous results from two-dimensional modeling are shown to be a special case of this general analysis when the multipath power and the travel direction are confined to a single plane in space. The results show that the main lobe of the spatial correlation of the signal envelope at a given distance has an approximately Gaussian dependence on the three-dimensional multipath directivity metric proposed in this paper, for both cases for the travel direction.

This paper develops a generalized theory of multipath shape factors used to study the small-scale fading statistics in three-dimensional non-omnidirectional multipath channels. Previous results for horizontal propagation channels are special cases of the present framework when the multipath angular power density (APD) and the travel direction of the mobile unit are confined to a plane. The three-dimensional multipath shape factors are derived in terms of the first three degrees of unnormalized spherical harmonics of the APD. Based on the so derived shape factors, analytical expressions for the level crossing rate, average fade duration and approximate envelope correlation are derived for a Rayleigh fading three-dimensional channel.