Introduction to Variational Mode Decomposition(VMD)

This will be a blog series because it's tough to cover everything in one blog. Please bear with me if things are confusing. Any doubts, the comments section is always waiting for you.

Let's start by asking a simple question.

Can you hear the instruments individually while listening to any music with your eyes close?

How do we do that?

Well, it seems we use different filters to focus our attention on a particular instrument. Interestingly, the filters are adaptable and can work while listening to any type of song. This method is known as source separation. There are multiple inputs combined and our ears are capable of separating them. Similarly, data from electrical grids, rotary machines, music signals, etc contains multiple components. The aim is to decompose or separate these multiple components.

The Motivation

The motivation for this blog is simple and clean. There is not much material available to understand VMD and mostly very few are even aware of such ideology. So let's learn something new today.

What is a Mode?

According to the aurthor[1], there is something called intrinsic mode function which is mathematically expressed as: