This paper describes an efficient pedestrian detection system for videos acquired from moving platforms. Given a detected and tracked object as a sequence of images within a bounding box, we describe the periodic signature of its motion pattern using a twin-pendulum model. Then a principle gait angle is extracted in every frame providing gait phase information. By estimating the periodicity from the phase data using a digital phase locked loop (dPLL), we quantify the cyclic pattern of the object, which helps us to continuously classify it as a pedestrian. Past approaches have used shape detectors applied to a single image or classifiers based on human body pixel oscillations, but ours is the first to integrate a global cyclic motion model and periodicity analysis. Novel contributions of this paper include: i) development of a compact shape representation of cyclic motion as a signature for a pedestrian, ii) estimation of gait period via a feedback loop module, and iii) implementation of a fast online pedestrian classification system which operates on videos acquired from moving platforms.