Automatic identification and categorization of Alzheimer’s patients and the ability to distinguish between different levels of this disease would be very helpful to the research community studying this disease since non-automatic approaches are both very time-consuming and highly dependent upon the experience of experts. Here, it is proposed that instantaneous cerebral phase and envelope information from functional magnetic resonance imaging data is of use to discriminate between Alzheimer’s patients, mild cognitively impaired subjects and healthy individuals. Following a region-of-interest analysis of functional magnetic resonance imaging data, different features including power, entropy, and coherency features are derived from the instantaneous phase and envelope signal sequences. Various sets of features are calculated and fed to a sequential forward floating feature selection algorithm to identify the most discriminative and informative feature sets. A Student’s t-test was employed to select the most relevant features from the sets. Finally, a K-nearest neighbor classifier is used to distinguish between classes in a three-class categorization problem. The reported performance in overall accuracy using functional magnetic resonance imaging data of 111 combined participants is 80.1% with 80.0% sensitivity for the distinction of both Alzheimer’s and healthy categories. This is comparable to the state-of-the-art approaches recently proposed for this task. The significance of obtained results was statistically confirmed by the evaluation of standard classification performance indicators. Results illustrate that the analytic phase and envelope feature indices derived from the region of interest signals described here are significant discriminators suited to distinguish between Alzheimer patients and healthy subjects.