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The purpose of this paper is to demonstrate the capabilities of continuous wavelet transform (CWT) in analyzing electroencephalogram (EEG) signals produced through a single-electrode recording device. Further, CWT is used to evaluate standard fast Fourier transform (FFT) analysis results. Sequential resting eyes-closed (EC) and eyes-open (EO) EEG signals, recorded from individuals during a one year period (N = 25), are analyzed. The absolute and relative geometric mean powers of the EEG δ, θ, α, and β-bands are calculated using FFT and CWT analysis. A sliding Blackman window based FFT analysis shows a statistically significant α and β-band dominant peaks for EC compared to EO recordings. These results confirm well-known results reported in the literature, which validates the EEG recording device. CWT analysis using Morlet mother function results are consistent with those of FFT analysis and revealed additional differences where a second range of statistically significant dominant scales are clearly observed in the δ-band for EO compared with EC, which has not been reported in the literature. However, the difference between EO and EC power spectra in the β range is less significant in the wavelet analysis.