The robustness of the Time Reversal (TR) scheme in a non stationary channel environment has been previously studied for Ultra-Wide Band (UWB) channels. However, its robustness with different bandwidth specially for bandwidths significantly lower than ultra-wide bandwidths has not been established. In this paper, the performance of a TR communication system has been studied for large number of bandwidths for both UWB and narrow band systems in a non-stationary channel environment. The results show that TR scheme gives a robust performance for both wide and narrow bandwidths. The performance of the TR scheme also gets better for higher bandwidths.