Two methods, power spectrum density analysis (PSD) and synchronization signal approximation, were investigated to determine if underlying periodic, free energy signals could be detected for the individual genes in this paper. These signals could be revealed assuming Watson-Crick type hybridization between the eight, 3'-terminal nucleotides of the 18S rRNA and pre- and mature-mRNA sequences in Saccharomyces cerevisiae in a manner similar to that used to analyze coding region sequences in prokaryotic genes. Using PSD, a periodic signal could only be detected in 35 of 106 genes tested; using the synchronization signal approximation, 91 of 106 genes showed linearly increasing magnitude and phase, characteristics consistent with the presence of an underlying periodic signal with an assumed frequency of one-third. The majority of introns did not show magnitude and phase behavior consistent with an underlying non-periodic signal. The periodicity property for the free energy on the protein-coding regions can contribute to finding the approximate boundaries of the exons (protein coding regions) and the introns, which provides a foundation for future studies in identifying the exact positions of the splice sites, especially for the higher eukaryotic genes.