Spike estimation from calcium (Ca2+) fluorescence signals is a fundamental and challenging problem in neuroscience. Several models and algorithms have been proposed for this task over the past decade. Nevertheless, it is still hard to achieve accurate spike positions from the Ca2+ fluorescence signals. While existing methods rely on data-driven methods and the physiology of neurons for modelling the spiking process, this work exploits the nature of the fluorescence responses to spikes using signal processing. We first motivate the problem by a novel analysis of the high-resolution property of minimum-phase group delay (GD) functions for multi-pole resonators. The resonators could be connected either in series or in parallel. The Ca2+ indicator responds to a spike with a sudden rise, that is followed by an exponential decay. We interpret the Ca2+ signal as the response of an impulse train to the change in Ca2+ concentration, where the Ca2+ response corresponds to a resonator. We perform minimum-phase group delay-based filtering of the Ca2+ signal for resolving spike locations. The performance of the proposed algorithm is evaluated on nine datasets spanning various indicators, sampling rates and, mouse brain regions. The proposed approach: GDspike, is compared with other spike estimation methods including MLspike, Vogelstein de-convolution algorithm, and data-driven Spike Triggered Mixture (STM) model. The performance of GDSpike is superior to that of the Vogelstein algorithm and is comparable to that of MLSpike. It can also be used to post-process the output of MLSpike, which further enhances the performance.