  In this work, we investigate the Hawking radiation in higher dimensional
Reissner-Nordstr\"om black holes as received by an observer, resides at
infinity. The frequency-dependent transmission rates, which deform the thermal
radiation emitted in the vicinity of the black hole horizon, are evaluated
numerically. Apart from the case of four-dimensional spacetime, the
calculations are extended to higher dimensional Reissner-Nordstr\"om metrics,
and the results are found to be somewhat sensitive to the spacetime dimension.
In general, it is observed that the transmission coefficients practically
vanishes when the frequency of the emitted particle approaches zero. It
increases with increasing frequency and eventually saturates to some value. For
four-dimensional spacetime, the above result is shown to be mostly independent
of the metric's parameter, neither of the orbital quantum number of the
particle, once the location of the event horizon, $r_h$, and the product of the
charges of the black hole and the particle $qQ$ are given. For
higher-dimensional cases, on the other hand, the convergence becomes more
slowly. Moreover, the difference between states with different orbital quantum
numbers is found to be more significant. As the magnitude of the product of
charges $qQ$ becomes more significant, the transmission coefficient exceeds
one. In other words, the resultant spectral flux is amplified, which results in
an accelerated process of black hole evaporation. The relation between the
calculated outgoing transmission coefficient with existing results on the
greybody factor is discussed.
