A method for obtaining the directional spectrum, on assuming that the frequencies of the elementary waves are all different from one another, is re-proposed in a form suitable for applications to sea states near a coast. The method is applied to an interval of 10h during which the sea state remained basically steady state off the beach at Reggio Calabria (east coast of the Straits of Messina). It is shown that the directional spectrum converges as the length of the time series data grows. A numerical simulation of a 10h sea state confirms that the directional spectrum converges as the length of the time series grows, and the convergence is onto the known directional spectrum used to make the numerical simulation. Through the numerical simulation, it is proved that the method, generally, is suitable for applications even with short time series of wind waves (duration of about 100T_p). Finally, it is shown that the method is not necessarily inadequate even with short records of multimodal sea states with different modal directions, modal amplitude ratios and intermodal distances.