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Hundreds of smartphone apps are monitoring users through their microphones
(www.the-independent.com)
This is a most excellent place for technology news and articles.
You could easily process the audio and filter in on the device and just send the transcribed parts that match your filters for further processing. No need to send a constant audio stream. Eventually it would show up in the battery usage but things like the google song recognition also heavily use the mic and process audio and it doesn't show up as heavy as you would expect.