Signal Processing Technique: Empirical Mode Decomposition

Empirical Mode Decomposition (EMD) is an essential signal processing technique that's especially useful when you're dealing with signals that change a lot over time where the amplitude, frequency, or even phase keep changing —what we call non-stationary signals. These are signals you come across in real life, like voice, music, and or stock data. Think of it as a way to break down these complex, ever-changing signals into simpler parts, which are like building blocks. These building blocks are called Intrinsic Mode Functions (IMFs), and they're unique because they adapt to the signal you're studying. 

These IMFs are a set of adaptive, non-stationary basis functions. This basically means each IMF is a simpler version of the original signal. The IMFs are shown in a set of plots, allowing you to see how the signal's amplitude and frequency change over time. You might be wondering, "How is this different from a spectrogram?".A spectrogram also shows you how frequency changes over time but with constraint of trading off time or frequency resolution. But EMD you see changes in both time and frequency without having to compromise on the resolution of either features.

It's incredibly useful for analyzing real-world, non-stationary signals like ECG data or stock market variations. By decomposing the signal into IMFs, you can focus on specific features of the signal. It gives you a way to interpret the underlying process more intuitively by correlate amplitude and frequency variation at each point in time.

IMF Top Plot

• Zero-crossings: These are the points where the IMF crosses the zero line. They are marked in purple and occur at specific times.

 Instantaneous Frequency (Bottom Plot)

• Purple Points: These points correspond to the zero-crossings in the IMF. The frequency value at these points is the estimated instantaneous frequency.

By looking at these plots, you can visually correlate the zero-crossings in the IMF (top plot) with their corresponding instantaneous frequencies (bottom plot). This shows how you can gain a localized understanding of the frequency content of the IMF at different times, providing both time and frequency localization.