Empirical Mode Decomposition (EMD) for EEG and PPG Signal Analysis Empirical Mode Decomposition (EMD) is a signal processing technique designed to break down non-linear and non-stationary signals into a set of intrinsic mode functions (IMFs). It is particularly effective for analyzing complex biological signals like electroencephalogram (EEG) and photoplethysmogram (PPG), which often involve multiple frequencies and varying amplitudes.

How EMD Works:

Sifting Process:

Local Extrema Identification: EMD starts by identifying all the local maxima and minima in the signal, which represent its peaks and troughs. Envelope Creation: Upper and lower envelopes are created by interpolating between the maxima and minima, respectively, forming smooth curves that capture the signal’s overall trend. Mean Calculation: The mean of these two envelopes is calculated. Signal Subtraction: This mean is subtracted from the original signal, yielding a new, more oscillatory signal focusing on specific frequency components. Repetition: The sifting process is repeated on this new signal until the resulting signal meets certain criteria, such as having a consistent number of zero crossings and extrema, making it an IMF. IMF Extraction:

First IMF: The first IMF is the result of several sifting iterations and represents the signal's highest frequency component. Residual Signal: After subtracting this IMF from the original signal, the residual signal is obtained. Subsequent IMFs: The residual signal undergoes the same sifting process to extract additional IMFs, each corresponding to progressively lower frequency components, until only a monotonic residual remains. Final Decomposition:

The output is a series of IMFs, each capturing an oscillatory mode within the original signal, allowing for a detailed multi-resolution analysis. Application in EEG and PPG Signals: EMD is particularly useful in EEG analysis, where it separates complex brain wave patterns like alpha, beta, delta, and theta waves into individual IMFs for detailed study. In PPG analysis, EMD helps isolate heart rate signals from noise and detect variations indicating potential cardiovascular issues. This makes EMD a powerful tool for extracting meaningful information from complex physiological signals.