This study broaches in a novel way the analysis of cognitive impairment characteristic of the early stages of Alzheimer's Disease (AD). Specifically, we attempt to determine the acoustic speech parameters that are sensitive to the onset of the disease, and their association with the language deficit characteristic of AD. Speech analysis was carried out on 21 elderly patients with AD using Praat software, which analyzes the acoustic components of speech. The data obtained were subjected to stepwise regression, using the overall scores obtained in the test as the criterion variable, and the scores on the frequency, amplitude and periodicity variables as predictors of performance. We found that the percentage of voiceless segments explains a significant portion of the variance in the overall scores obtained in the neuropsychological test. This component seems to be related mainly to the patient's ability in phonological fluency. This finding could permit the creation of a diagnostic test for AD through analysis of the acoustic speech parameters at very low cost in terms of both time and resources.