[Idea] Fourier transforms to Identify per-device power consumption?

I was looking at the power graph on my HA from my Shelly power monitor and realised that I could identify some devices by their characteristic shape on the graph.
It made me wonder, would it be possible to use Fast Fourier Transforms to identify the state and power consumption of various devices simply from the power/time graph.

For very simple use cases, it might be possible. After all, spectral analysis is a rich field.

But in real-world applications it is not so easy to detect devices by analysis of power use. For example, heaters often work by cycling on and off. The frequency of on/off cycles depends on how close the heater is to the control point. With more than one heater on the same circuit, it is difficult to distinguish one heater from another. And heaters have very simple power signatures.

I have a Sense Home Energy Monitor on my mains (and solar input). Sense was founded by experts in signal processing with extensive experience in voice recognition. They advertise smart device detection using advanced analysis and AI/ML. You will find in the forums that most users complain that this feature doesn’t work well. It’s simply a very difficult problem.

Monitoring individual circuits would simplify the problem. But it would be easier in general to put individual power monitors on key devices and use that instead.