Accurate estimation of spike train from calcium (Ca2+) fluorescence signals is challenging owing to significant fluctuations of fluorescence level. This paper proposes a non-model-based approach for spike train inference using group delay (GD) analysis. It primarily exploits the property that change in Ca2+ fluorescence corresponding to a spike can be characterized by an onset, an attack, and a decay. The proposed algorithm, GDspike, is compared with state-of-the-art systems on five datasets. F-measure is best for GDspike (41%) followed by STM (40%), MLspike (39%), and Vogelstein (35%). While existing methods are inspired by the physiology of neuronal responses, the proposed approach is inspired by GD-based high-resolution processing of the Ca2+ fluorescence signal. GDspike is a fast and unsupervised algorithm. It is unaffected by the scanning rate and indicator protein/dye.