We consider the task of automatic classification of healthy subjects and patients with essential vocal tremor (EVT) from a recording of sustained phonation. For the classification task, we propose a new set of acoustic features called pitch oscillation characteristics (POC) using empirical mode decomposition of high resolution pitch contour and its derivative. Classification experiments are performed on 25 healthy controls (HC) and 20 EVT patients using a support vector machine classifier and the proposed POC features. Experiments are also performed using a set of baseline features computed from the multi-dimensional voice program (MDVP). Classification accuracy obtained from the human experts are used for comparison too. The classification accuracy from human expert is found to be better than those from the automatic classification. However, it is found that, the average classification accuracy using a combination of the POC and baseline features is 63.66 % closer to the classification accuracy obtained from the experts compared to that using baseline features alone.