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This paper points out that no existing technically-implemented speech model is adequate enough to describe one of the most fundamental and unique capacities of human speech processing. Language acquisition of infants is based on vocal imitation but they don't impersonate their parents and imitate only the linguistic and para-linguistic aspects of the parents' utterances. The vocal imitation is found only in a few species of animals: birds, dolphins, and whales, but their imitation is basically acoustic imitation. How to represent exclusively what in the utterances human infants imitate? An adequate speech model should be independent of the extra-linguistic features and represents only the linguistic and para-linguistc aspects. We already proposed a new speech model, called speech structure, which is proved mathematically to be invariant with any kind of transformation. Its extremely high independence of speaker differences was shown experimentally. In this paper, by reviewing studies of evolutionary anthropology and language disorders, we discuss the theoretical validity of the new model to describe the human-unique capacity of speech processing.