I suppose that would work, but the lady asked for a wireless link and a loud signal that could wake a possibly sleeping caregiver. It also needed to ignore background noise, like her husband's favorite radio program. There are of course, many ways to skin a cat, each with its own set of advantages and disadvantages.
There may be another approach to this. A miniature voice recorder, like the Sony IDC-BX700, has a VOR mode (Voice Operated Record). The earphone output can be fed to a small amplifier/speaker which can be located in the caregiver's room. This eliminates the possibility of feedback. The recorder would be placed in the Record mode with VOR, close enough to the patient's mouth. One would adjust the threshold of the VOR and/or distance to the person. Recorders have a microphone input also, so a mic can be easily positioned if the recorder can't be conveniently placed. The battery consumption is low when in VOR mode. Some recorders also have a DC supply input (for a wall wart).
This device is intentionally designed so that it does not have to be tuned to anyone's voice. The design should be marketable just as it is. If you set the low-pass filter (LPF) to 1000Hz and the gap to 50mS, it would respond to anyone's voice (male or female). I have switches to lower the LPF to 500Hz and the gap to 15mS to get the maximum possible rejection of background noise. The system still does an excellent job of rejecting background noise at 1000Hz and 50mS. Any sound that passes through the LPF and is uninterrupted for 1.5 seconds will trigger it.
I tested it in my house with blaring loud music in the background and, depending on the location of the speakers relative to the microphone, it would respond to my voice only and not the music. I have sinus trouble, which sometimes causes my voice to break up. Feeling that a patient might have the same problem, I added a switch to set the maximum gap width to 50mS. If you didn't want to put any switches in it, I would set the LPF to 1000Hz and the gap width to 50mS. The noise-cancelling microphone helps a lot as well.
And I do hope that the sound acquisition and the filtering system of this device is robust and flexible, because practically every person will have different stroke groan at different frequency, I hope they have catered for this problem in a more generalized & effective way. So that it proves to be marketable.
What a great innovation by andrew, this might become the basis of saving limitless human lives in the future. I do hope it soon comes out into a product form so that it can actually do some good to us.
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