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Originally Posted by Tuee
Yes, you're right—I see it now. An omni-directional microphone will almost certainly pickup more signal than one only looking in one direction,
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That's exactly where I claim it's wrong.
It will pick up the same amount of signal as a correctly aimed directional receiver, but it will pick up noise from everywhere in addition to what the directional picks up.
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but obviously it won’t have any directional information about it. The argument that the omni-directional microphone “drowns in noise coming from all directions” is incorrect—it will pick up more of everything, including the signal.
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It's the same amount of SIGNAL acoustical energy arriving at the sensor, while the directional one ignores NOISE acoustical energy from everywhere else.
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To put it in statistical terms, because the “sample” is larger, the power of the test is much stronger. The return-ping ought to “jump out” more against the background of all that sampled data.
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Remember that what you're looking for, in statistical terms, is an aberration. (I think statistics one uses another word? Doesn't really matter though.)
Which of these stand out?
1 2 4 3 6 1 5 3 15 5 4 2
Then, which one stands out here?
12 11 15 9 15 13 19 12 15
And now the next clue - which one stands out THE MOST?
Following up, that sequence presumed the signal itself was rather strong - it produced a 15 vs an otherwise high at 6. If it's weak, the additional variations introduced by the extra noise will bury it.
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So LuftWolf is right—a weaker return can’t contain more information than a stronger return,
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Which has nothing to do with the discussion. The return contains the amount of information it does, the issue is how its interpretion (or lack thereof) removes information from it.
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and an omni-directional microphone has the best chance of picking up a weak return.
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This is the point I disagree with. Why did extending a wlan over 5km require directional antennas, when omni would be better at detecting weak signals? They didn't use one of each on each side either.
Your discussion of the human eye gave me an idea: I think the reason it can
sometimes be heard before seen in real life, (that was what they said, wasn't it?) would be an effect of small 'beam width'. Sound doesn't originate from a single point, nor does it move in a straight line. If the sound takes multiple paths that has it arriving from several directions at the same time, and the 'beam width' of the directional receiver isn't big enough to catch them all as in the same direction, while an omni receiver will. That would be the only situation in which an omni receiver should get a stronger signal strength than a directional.