I'm looking for some method to control an Arduino with voice commands.
Could this work on this platform?
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Yes possible on some of the high end Arduinos, but I know of no example where it has been done. The quality of recognition will be proportional to the processing power provided. In the case of an Arduino, probably not at an acceptable level.
You would be much better off looking at the multitudes of PC solutions, and using the Arduino as an interface to what ever it is you plan on controlling.