This paper introduces the Local Mean Decomposition (LMD), a novel iterative method for demodulating amplitude and frequency-modulated signals. LMD decomposes such signals into a set of functions, each consisting of an envelope signal and a frequency-modulated signal, allowing the derivation of a time-varying instantaneous frequency. The method is applicable to various natural signals, including electroencephalograms (EEGs), functional magnetic resonance imaging data, and earthquake data. The paper applies LMD to EEG data from a visual perception experiment, examining the instantaneous frequency and energy structure of the EEG and comparing it with spectrogram results. The analysis reveals statistically significant differences in the degree of instantaneous phase concentration between perception and non-perception EEG data, suggesting that LMD provides a robust and physically meaningful way to analyze complex biological signals. The LMD approach is particularly useful for understanding the frequency and energy structure of EEG signals, which are correlated with specific cognitive states.This paper introduces the Local Mean Decomposition (LMD), a novel iterative method for demodulating amplitude and frequency-modulated signals. LMD decomposes such signals into a set of functions, each consisting of an envelope signal and a frequency-modulated signal, allowing the derivation of a time-varying instantaneous frequency. The method is applicable to various natural signals, including electroencephalograms (EEGs), functional magnetic resonance imaging data, and earthquake data. The paper applies LMD to EEG data from a visual perception experiment, examining the instantaneous frequency and energy structure of the EEG and comparing it with spectrogram results. The analysis reveals statistically significant differences in the degree of instantaneous phase concentration between perception and non-perception EEG data, suggesting that LMD provides a robust and physically meaningful way to analyze complex biological signals. The LMD approach is particularly useful for understanding the frequency and energy structure of EEG signals, which are correlated with specific cognitive states.