Hi all,
For the record, I want to clarify once again why it's a good idea to set
the audio level so low that 16-bit digitized samples of pure background
noise have an rms range around 30.
Seemingly very reasonably, Mike asked why would we not want to set the
level higher, thereby using more bits and having a closer digital
approximation of the underlying analog signal.
On 3/2/2017 3:40 PM, Black Michael wrote:
> We've got 90dB of space to work with. Why would we NOT want the dynamic
> range? ...more dynamic
> range means more accurate FFTs and such, doesn't it?
Suppose the background noise level has been set to give rms=30 for the
digitized data. The average "power" is then the square of this value,
i.e. 900.
A small portion of this 900 units of power comes from quantizing noise
in the A/D process. How small a portion? Ideally the largest
quantizing errors fall in the range -0.5 to +0.5, i.e., half of a
least-significant bit. So the "power" in the quantizing noise is less
than 0.5^2 = 0.25.
Maybe the A/D is kinda lousy, so the amplitude errors are twice as big
and the "power" in quantizing noise thus four time as big, i.e. 1.0.
This means that our 900 units of measured power are 899 units of
background noise and 1 unit of quantizing noise.
OK: so how much S/N is lost as a result of the quantization errors? The
signal level S is unchanged. In this worst possible case, the noise is
increased from 899 to 900 units. The loss of S/N (in dB) is therefore
10*log10(900/899) = 0.0048 dB.
If you can set the level for background noise significantly higher than
30 dB and still not run out of headroom when strong signals or strong
impulsive noise are present, there is no harm in doing that. But you
won't gain more than about 0.005 dB in your quest to decode weak signals.
-- 73, Joe, K1JT
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