In this study, we investigate the Hawking radiation in higher dimensional Reissner-Nordstrm black holes as received by an observer located at infinity. The frequency-dependent transmission rates, which deform the thermal radiation emitted in the vicinity of the black hole horizon, are evaluated numerically. In addition to those in four-dimensional spacetime, the calculations are extended to higher dimensional Reissner-Nordstrm metrics, and the results are observed to be sensitive to the spacetime dimension to an extent. Generally, we observe that the transmission coefficient practically vanishes when the frequency of the emitted particle approaches zero. It increases with frequency and eventually saturates to a certain value. For four-dimensional spacetime, the above result is demonstrated to be mostly independent of the metric's parameter and the orbital quantum number of the particle, when the location of the event horizon, , and the product of the charges of the black hole and the particle qQ are known. However, for higher-dimensional scenarios, the convergence becomes more gradual. Moreover, the difference between states with different orbital quantum numbers is observed to be more significant. As the magnitude of the product of charges qQ becomes more significant, the transmission coefficient exceeds 1. In other words, the resultant spectral flux is amplified, which results in an accelerated process of black hole evaporation. The relationship of the calculated outgoing transmission coefficient with existing results on the greybody factor is discussed.