Hi, There are actually some quite polished EMG sensors if you need them, like this one: https://www.adafruit.com/product/2699
But to answer your questions:
I think it's save to say that with a 3 x 3 x 1 inch battery pack you'd be totally safe though, and you could probably get away with a lot less.
Yes, you could definitely do some analysis. The JS code isn't very fast for ploughing though data, but there are things like built-in FFT, so you could run the data through that and pick out potential frequencies of interest very easily. There's also compiled JS code or the ability to just write some C code if you had to do some very heavy analysis.
I think the WiFi would be fine - the other option is something like Puck.js. If you could cut down on the amount of data sent (for example doing an FFT and sending only some parts of it) then it could be a definitely option and is much smaller. It's very likely that one battery would last you well over a night - although it depends on how much power the EMG draws
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