Marine mammals use sound for communication and echolocation within their ecosystems. The detection of these sounds is an important aspect of signal processing, such that we can estimate the spatial position and direction of arrival of these mammals, and have an understanding of their ecology. Passive acoustic monitoring (PAM) is widely used to understand marine mammal movement and vocal repertoire. In PAM, datasets are accumulated over days, months or years. Thus, it is impracticable to manually analyse the datasets because it is very large. This motivated the development of automated sound detection techniques for marine mammals, which most often varies depending on the vocal duration, frequency range and call type. In this paper, continuous recordings of Bryde's whale (Balaenoptera edeni edeni) short pulse calls (<; 3.1s long) were collected on a weekly basis from December 2018 to April 2019 on sighting of the individual in a single site in the endmost South-West of South Africa. The sound, previously not documented off South Africa, was observed on visual confirmation of the presence of inshore Brydes's whale. In addition, the paper develops and analyses two automated template-based detection algorithms for this short pulse call, employing dynamic time warping (DTW) and linear predictive coding (LPC) techniques. These proposed template-based detectors are novel, as they have not being previously used in Bryde's whale sound detection in the literature. When applied to the continuous recordings of the short pulse calls, the DTW-based and LPC-based detection algorithms obtained a sensitivity of 96.04% and 97.14% respectively for high signal-to-noise ratio (about 10dB above the ambient sound). Otherwise, for low SNR, the DTW-based and LPC-based detection algorithms obtained a sensitivity of 94.98% and 96.00% respectively. These detection algorithms exhibit low computational time complexity and can be modified to analyse the movement of obscure but vocal marine species instead of manual identification.