Abstract: The framework of Finite Rate of Innovation (FRI) is an effective theory for sampling and reconstruction of non-bandlimited signals. However, the method may be invalid when the pulse shape is complex, since it requires that the frequency spectrum of pulse must meet some special requirements. In this paper, a FRI sampling system based on exponential reproducing kernels is introduced. It has an outstanding advantage that the adaptability for pulse shape can be increased by adjusting the parameters of sampling kernel. On the other side, from implement and stability points of view, the parameters are constrained by extra factors, which are detailedly analyzed, and the guidance of choosing right parameters is given out. Simulations are conducted on hybrid LFM and phase code pulse streams, and the results verify the validity of the proposed method.