The paper introduces a new method for analyzing nonlinear and non-stationary time series data, focusing on empirical mode decomposition (EMD) and the Hilbert spectrum. The key innovation is the concept of "intrinsic mode functions" (IMFs), which are derived from the local characteristic time scales of the data. These IMFs admit well-behaved Hilbert transforms, allowing for the calculation of instantaneous frequencies. The Hilbert spectrum, an energy-frequency-time distribution, is then constructed from these IMFs, providing a localized representation of the data's energy content over time. The method is adaptive and efficient, making it suitable for complex, nonlinear, and non-stationary processes. The authors demonstrate the effectiveness of this approach through numerical examples and natural phenomena data, highlighting its advantages over traditional Fourier spectral analysis, which is limited to linear and stationary systems. The paper also reviews existing methods for non-stationary data processing, such as spectrograms, wavelet analysis, and evolutionary spectrum, and discusses their limitations. The EMD method is shown to be a powerful tool for analyzing nonlinear and non-stationary data, offering a more accurate and physically meaningful representation of the data's energy-frequency-time distribution.The paper introduces a new method for analyzing nonlinear and non-stationary time series data, focusing on empirical mode decomposition (EMD) and the Hilbert spectrum. The key innovation is the concept of "intrinsic mode functions" (IMFs), which are derived from the local characteristic time scales of the data. These IMFs admit well-behaved Hilbert transforms, allowing for the calculation of instantaneous frequencies. The Hilbert spectrum, an energy-frequency-time distribution, is then constructed from these IMFs, providing a localized representation of the data's energy content over time. The method is adaptive and efficient, making it suitable for complex, nonlinear, and non-stationary processes. The authors demonstrate the effectiveness of this approach through numerical examples and natural phenomena data, highlighting its advantages over traditional Fourier spectral analysis, which is limited to linear and stationary systems. The paper also reviews existing methods for non-stationary data processing, such as spectrograms, wavelet analysis, and evolutionary spectrum, and discusses their limitations. The EMD method is shown to be a powerful tool for analyzing nonlinear and non-stationary data, offering a more accurate and physically meaningful representation of the data's energy-frequency-time distribution.