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Tweakers' Asylum Tweaks for systems, rooms and Do It Yourself (DIY) help. FAQ. |
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Tweakers' Asylum Tweaks for systems, rooms and Do It Yourself (DIY) help. FAQ. |
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In Reply to: Re: Um... posted by JohnR on December 30, 2001 at 14:36:10:
Thanks Steve. I also asked a friend who's in the digital audio field and he said the same:
Nope. The smallest possible signal is a single quantum (eg,
0 to 1) and the largest 2^16, regardless of whether the
encoding is signed or not, hence a 96 dB dynamic range.
The signal +/- 1 is twice as big as the smallest possible
signal.
It doesn't match my intuitive thinking about how the signal is represented (ie +/- 1), but I guess my intuition is wrong :-)Yeah, intuition can get ya. Some of my most embarrassing moments have come about because I put too much faith in intuition and didn't bother to actually work it out before I opened my mouth. :)
The +/- thing is a bit easier to understand when you look at it in terms of differences. The difference between +1 and -1 is 2. And of course difference is simply the result of a mathematical subtraction operation. So (+1) - (-1) = 2, (+2) - (-2) = 4, and so on.
An amplifier with a differential input, a basic opamp for example, has two input terminals, one non-inverting (desginated with a + sign) and one inverting (designated with a - sign). A differential amplifier only amplifies the difference it sees between its two input terminals as referenced to ground by subtacting the two values it sees at each input.
So if you use such a differential amplifier and configure it as a balanced input, and feed one signal into one input and another signal, of the same magnitude but of opposite polarity into the other input, the subtraction of these two signals results in an ouput signal that's twice the magnitude of each individual signal (assuming of course the opamp's configured for unity gain or a gain of 1).
It's also this subtraction which gives such an input the ability to reject common-mode signals such as those due to interference. Any two signals of the same magnitude and polarity at the opamp's input results in an output of 0 as 1 - 1 = 0.
Mathematical operations on signed numbers isn't terribly intuitive, but once you "get it" it's one of those forehad-smacking "D'oh!" things. :)
se
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Follow Ups
- Re: Um... - Steve Eddy 23:07:09 12/30/01 (0)
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