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[AUDITORY] angular resolution of microphones' matrices



Dear Auditory List,
 
In the upcoming future I begin a project focused on creating a small driver aimed to control home devices. It will be voice-controlled, hence a small microphone matrix have to be implemented in it. I’ve made some preliminary research in the topic of matrices, but I haven’t found an answer to my most important question: is there any equation or, let’s say, ‘simple law’, which let estimate angular resolution (both horizontally and vertically) of the matrix regarding number of microphones and geometry between them? Maybe you can advise me something or just point out papers and research which I should analyze? And what about programming it effectively using real-time processing? I will probably use MEMS microphones, maybe this information helps you somehow. I will really appreciate your help.
 
Best regards from Poland,
Jan Felcyn, Institute of Acoustics, Adam Mickiewicz University, Poznań, Poland