A new model for sparse time dispersive channels in pilot aided OFDM systems is developed by considering prior knowledge on channel time dispersions. Weighted atomic norm minimization is implemented in the model which enables a more accurate channel estimation. The channel response is identified by solving a Least Squares problem. In this work, we assume that time dispersions' associated frequencies can take any value with a minimum distance on the normalized interval $[0,1)$. The performance of the new model is compared with conventional approaches. With respect to pilot number and SNR, the simulation results reveal that the new model performs superior to that of conventional methods. It is shown that both a lower energy and pilot number are required to achieve the same symbol error rate (SER) reported in previous works.