This paper introduces the Local Mean Decomposition (LMD), a new method for demodulating amplitude and frequency modulated signals. LMD decomposes such signals into a set of functions, each being the product of an envelope signal and a frequency modulated signal, from which a time-varying instantaneous frequency can be derived. The method is applied to analyze EEG data from a visual perception experiment, where subjects viewed a running figure made of black dots on a white background. The results show statistically significant differences in theta phase concentrations between perception and no perception EEG data. LMD is compared with other methods like the spectrogram and Hilbert spectrum. The LMD method provides a time-varying frequency and energy representation of the EEG, which is more accurate than traditional Fourier-based methods. The LMD approach decomposes EEG data into product functions, each with an associated envelope and instantaneous frequency, allowing for a detailed analysis of the signal's time-frequency-energy structure. The study reveals that the LMD method effectively captures the time-varying frequency and energy of the EEG, particularly in the theta and gamma bands. The results show that the LMD method provides a more accurate representation of the EEG data compared to the spectrogram and Hilbert spectrum. The LMD method is also more computationally efficient than the short-time Fourier transform (STFT), although it requires multiple iterations to achieve a stable result. The paper concludes that LMD is a robust and conceptually simple method for analyzing amplitude and frequency modulated signals, particularly in the context of EEG data. It provides a physically meaningful time-varying frequency and energy representation of the data, which is more accurate than traditional Fourier-based methods. The LMD method is particularly useful for analyzing complex biological signals like EEG, where the frequency and energy structure is closely related to cognitive states. The results of this study suggest that LMD can provide new insights into the frequency and energy structure of EEG and other biological signals.This paper introduces the Local Mean Decomposition (LMD), a new method for demodulating amplitude and frequency modulated signals. LMD decomposes such signals into a set of functions, each being the product of an envelope signal and a frequency modulated signal, from which a time-varying instantaneous frequency can be derived. The method is applied to analyze EEG data from a visual perception experiment, where subjects viewed a running figure made of black dots on a white background. The results show statistically significant differences in theta phase concentrations between perception and no perception EEG data. LMD is compared with other methods like the spectrogram and Hilbert spectrum. The LMD method provides a time-varying frequency and energy representation of the EEG, which is more accurate than traditional Fourier-based methods. The LMD approach decomposes EEG data into product functions, each with an associated envelope and instantaneous frequency, allowing for a detailed analysis of the signal's time-frequency-energy structure. The study reveals that the LMD method effectively captures the time-varying frequency and energy of the EEG, particularly in the theta and gamma bands. The results show that the LMD method provides a more accurate representation of the EEG data compared to the spectrogram and Hilbert spectrum. The LMD method is also more computationally efficient than the short-time Fourier transform (STFT), although it requires multiple iterations to achieve a stable result. The paper concludes that LMD is a robust and conceptually simple method for analyzing amplitude and frequency modulated signals, particularly in the context of EEG data. It provides a physically meaningful time-varying frequency and energy representation of the data, which is more accurate than traditional Fourier-based methods. The LMD method is particularly useful for analyzing complex biological signals like EEG, where the frequency and energy structure is closely related to cognitive states. The results of this study suggest that LMD can provide new insights into the frequency and energy structure of EEG and other biological signals.