Demystifying the maths behind electronic warfare
10 Apr 24
Electronic Warfare
BY Luke Cabot
Our electronic warfare expert, Luke Cabot, explains the principle of Stare Time and frequency resolution from his local sauna
Windows, time, and electronic warfare (EW) - not an operating system and hours of colouring-in spreadsheet boxes (if you know, you know) but a curious paradox of measurement, and one I’ll use to introduce some of the fundamentals of EW.
I love demonstrating the virtually inexplicable in simple terms.
So, there’s a sauna in my local gym with a narrow window in it. I’m sat in there one day minding my own business and had a curious thought. If you look through the sauna window in just the right place, you can see the end of the swimming pool and people swimming left and right.
Then I thought, when the swimmers exit your field of view through the window, what happens to them? You might assume they are doing lengths. But are you certain? Maybe they got out. Perhaps they turned another way. Maybe they just stopped.
In all probability, they are likely swimming lengths. But what we find is this. Given a fixed window of observation, our measurement contains an element of un-certainty. To a lesser probability, the swimmers may indeed have got out or done something strange! How do we increase our certainty of what the swimmers are doing? We make the window bigger! So, a smaller window increases our un-certainty and a bigger one decreases it. If we could see the whole pool, well we would be absolutely certain of what the swimmers were doing. But in maths this is the equivalent of looking for all infinity and is not allowed!
In the world of EW, imagine the window is a fixed time interval that we call Stare Time, and the swimmers are the radio frequencies we wish to measure
In the world of EW, imagine the window is a fixed time interval that we call Stare Time, and the swimmers are the radio frequencies we wish to measure. The longer the Stare Time, the more certain we are of the radio frequency; our resolution has improved. But here is the paradox; if Stare Time gets small then frequency resolution (uncertainty) gets large. The obvious answer then is to make Stare Time as long as possible… but often you do not have this luxury in EW! If you get this, you now understand the principle of something called spectral leakage.
The enabling maths behind this paradox is the Fourier Transform, which shows that when something is big in time, it gets small in frequency and vice versa. If you understand the maths, then great! If you don’t, no worries, enjoy the show and remember the sauna window!
Fourier Transform shows that when something is big in time, it gets small in frequency and vice versa
I would like to thank all the gym staff for letting me do maths in the sauna and I hope in return you now understand the principle of Stare Time and frequency resolution.
If I’ve piqued your interest and you’d like to learn more, our Fundamentals of Air Electronic Warfare course is open to all individuals.
Taking place in Lincoln (UK) from 13-17 May, it’s set to be a fun and engaging training experience, full of hands-on demonstrations and everyday examples, to help you understand the air electromagnetic environment and its application via EW within military operations.
You can find out more, or signup, via email at [email protected].
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