The paper presents a novel technique of nonlinear spectral analysis, which has been used for processing encephalograms of humans. This technique is based on the concept of generalized entropy of a given probability distribution, known as the Rényi entropy that allows defining the set of generalized fractal dimensions of encephalogram (EEG) and determining fractal spectra of encephalographic signals. Unlike the Fourier spectra, the spectra of fractal dimensions contain information of both frequency and amplitude characteristics of EEG and can be used together with well-accepted techniques of EEG analysis as an enhancement of the latter. Powered by volume visualization of the brain activity, the method provides new clues for understanding the mental processes in humans.