Other than the topic of my master's thesis, Decomposition-based Quantitative EMG (DQEMG) is an analytical process by which the electrical signal from a muscle is decomposed into waveforms that represent the contributing Motor Unit Action Potentials, or MUAPs. Typically then, quantitative characteristics of those MUAPs (or also of the actional potential trains that are the series of MUAPS involved in a single muscle contraction that come from each motor unit) are used to contribute to (or eliminate) possible diagnostic conclusions as to the health or particular condition of the muscle.
If you want to understand it in detail, read this overview of motor units, which features this nice pictorial outline of decomposition.
My usual two-minute explanation goes something like this:
Most people are familiar with an ECG - electrocardiogram. You see them all the time on TV - the little monitor signal from the heart that goes blip, blip, when the patient is still alive. The heart is unique among the muscles in the body - when it contracts, all the muscle fibers in that part of the heart contract at once, giving that single blip for each contraction. The other muscles in the body, in order to do sustained contractions to lift or hold something, are organized into motor units - groups of muscle fibers that contract repeatedly, at different times, so that their contractions aggregate into the single muscle movement or effort we see from the outside. When you look at the electrical signal from that, you see a jaggedy combination of the signals all overlapping one another, called an interference pattern, or IP. When the muscle is fatigued, or a person is sick, you can start to see the effect of different motor unit contributions, as muscle contractions get more shaky or jittery and less smooth. That's because either the motor units are getting less coordinated or disproportionately weak and strong, or fewer of them are getting recruited to work.
Each motor unit is run by a single nerve, and diseases that affect muscle function can either be myopathies, affecting the muscle fibers, or neuropathies, affecting the nerves or the nueromuscular junction. Different neuromuscular diseases (as they are all called) lead to different observable characteristics in EMG. What a doctor usually does with an EMG signal is look at the interference pattern of the signals from all the motor units operating at the same time. More importantly, a doctor will listen to the signal - complexities or overly large MUAPs can be heard as high frequency noise or dull thuds, for example. An EMG signal is a sensitive diagnostic indicator - the trained human ear can pretty easily distinguish between a healthy EMG and an unhealthy one. What it is not is a specific indicator. DQEMG attempts to pull information out of the EMG signal that can be used to support more specific conclusions about the neuromuscular condition of a patient.
My favorite thing about my thesis work was figuring out how to display that quantitative information in such a way that patterns in it could effectively be interpreted by doctors, who are trained to listen to EMG and to look at obvious patterns in the IP, not to understand obscure indices that combine quantitative characteristics of MUAPs. Ultimately I proposed a radial display where each axis was normalized so that a healthy patient's signals would produce a round symetrical shape, whereas myopathy and neuropathy would produce distinctly different shapes, even in cases that are normally hard to distinguish from one another.