We investigate the sunspot area data spanning from solar cycles 1 (March 1755) to 23 (December 2010) in time domain. For this purpose, we employ the Hilbert transform analysis method, which is used in the field of information theory. One of the most important advantages of this method is that it enables the simultaneous study of associations between the amplitude and the phase in various timescales. In this pilot study, we adopt the alternating sunspot area as a function of time, known as Bracewell transformation. We first calculate the instantaneous amplitude and the instantaneous phase. As a result, we confirm a ~22-year periodic behavior in the instantaneous amplitude. We also find that a behavior of the instantaneous amplitude with longer periodicities than the ~22-year periodicity can also be seen, though it is not as straightforward as the obvious ~22-year periodic behavior revealed by the method currently proposed. In addition to these, we note that the phase difference apparently correlates with the instantaneous amplitude. On the other hand, however, we cannot see any obvious association of the instantaneous frequency and the instantaneous amplitude. We conclude by briefly discussing the current status of development of an algorithm for the solar activity forecast based on the method presented, as this work is a part of that larger project.