This paper presents the efficient systematic methods for modeling and analysis of spike signal sequence in crossbar arrays for neuromorphic computing chips. A novel spike signal sequence is proposed, where the ideal spike sequence with only spike time information in the original spiking neural network (SNN) algorithm is mapped onto actual spike waveform by stitching neighboring sequential spikes together with certain overlaps. We thoroughly investigate and analyze the performance of the input encoding as well as the implementation of spike timing dependent plasticity (STDP)-based SNN on memristor crossbar arrays with the proposed spike signal sequence. A detailed circuit model of a crossbar array, consisting of resistance, capacitance and inductance derived by the partial equivalent element circuit (PEEC) method, is created to simulate the training process of SNN. The proposed spike signal sequence is demonstrated that is able to achieve accurate input encoding as well as high recognition accuracy when it is used to perform the classification task on MNIST handwritten digits. The spike signal sequence is further analyzed and assessed in terms of the main factors affecting its encoding accuracy and the parasitic effects of crossbar arrays on its robustness.