In this paper, a series of simulations are performed with the lattice Boltzmann method (LBM) to analysis the spectral patterns of Nusselt number (Nu) in the RBC of air within a 2D closed square under Ra=1.0×10⁴~10⁹. The waved data of average Nu and local Nu on hot wall are probed as the source signals with time-dimensionless unit. The power spectrum densities (PSDs) of average Nu and local Nu indicate that the peak frequency varies among several discrete spectrum levels with the increase of Ra. Compared the spectra of the average Nu and local Nu, it is found that the spectrum of average Nu is not the weighted mean of local Nu spectra across hot wall, and the judgment of the peak frequency differs according to the two results. The main reason is that the average Nu smooths the fluctuation of data, and then it is difficult to capture the signal caused by the strong flow structures periodically crossing the hot wall. In contrast, the usage of local Nu signals to study RBC spectral features can yield more accurate and detailed information.