As part of the 2015 PhysioNet/CinC Challenge, this work aims at lowering the number of false alarms, which are a persistent concern in the intensive care unit. The multimodal database consists of 1250 life-threatening alarm recordings, each categorized as a bradycardia, tachycardia, asystole, ventricular tachycardia or ventricular flutter/fibrillation arrhythmia. Based on the quality of available signals, heart rate was either estimated from pulsatile waveforms (photoplethysmogram and/or arterial blood pressure) using an adaptive frequency tracking algorithm or computed from ECGs using an adaptive mathematical morphology approach. Furthermore, we introduced a supplementary measure based on the spectral purity of the ECGs to determine if a ventricular tachycardia or flutter/fibrillation arrhythmia has taken place. Finally, alarm veracity was determined based on a set of decision rules on heart rate and spectral purity values. Our method achieved overall scores of 76.11 and 85.04 on the real-time and retrospective subsets, respectively.