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/geometric-algebra- classifier/GAclassifier/. ; Shengling Zhou, Dimitar G. Valchev, Alex Dinovitser, James M. Chappell, Azhar Iqbal, Brian Wai-Him Ng, Tak W. Kee, and Derek Abbott