This paper explains the principles and provides examples of a new method for distinguishing between FAKE human speech synthesized by generative AI and natural speech. Since synthetic speech is generated based on information from a limited set of training spectra, the variety of vowels - which are key to identifying individuals - is limited. In contrast, natural speech exhibits a more diverse distribution of vowel spectra due to the flexibility of the human articulatory organ. In this paper, using Japanese - a Syllabary limited to five vowel phonemes, each of which corresponds one-to-one with a specific sound - as an example, we outline a method for distinguishing between synthetic and natural speech reading the same text by analyzing the spectral distributions. If we normalize the spectra of speech sounds and regard them as probability density functions for the frequency bands received by the hair cells of the human cochlea, and evaluate the distance between spectra using the Wasserstein metric, the Wasserstein distances between the vowels of synthetic speech are short. By preserving this distance and performing a topological mapping using persistent homology, the spectral probability density functions of synthetic and natural speech can be decomposed into clusters.

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