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Signal to noise ratio semantics
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ejeffrey:
A ratio is a fraction, or just a number.  Don't get caught up on the A : B, that is just a way of expressing a number.  An SNR of 10 is high an SNR of 0.1 is low.  Or whatever, maybe you have different thresholds since high and low are somewhat situation dependent, but the import thing is not to get caught up on an SNR of 0.1 being 1 : 10 and thinking that because the 10 is large the "ratio" is large.

There is rarely a reason to express real world SNR in specific fractions like 13 / 7.  Those sometimes come up in mathematical proofs, such as a formula for the theoretical maximum SNR of a given system, but we don't usually measure them that way.  On the other hand with mechanical gear ratios we are often dealing with some integer number of gear teeth so it can be important to preserve the exact ratio rather than just convert to decimal and round.  But it is still the case that a gear ratio of 1/73 is a very low ratio, not high.
fourfathom:

--- Quote from: TimFox on August 30, 2022, 03:50:00 pm ---When translated into dB, a ratio <1 is a negative dB value.
--- End quote ---

This is the key point if we want to answer the OP's question.  We use dB when discussing SNR.  A negative number is considered to be lower than a positive number.  Can't get much simpler than that.
SiliconWizard:

--- Quote from: eugene on August 30, 2022, 12:52:02 pm ---
--- Quote from: Circlotron on August 30, 2022, 05:26:17 am ---The confusion stems from the terms LOW and HIGH.

noun: ratio; plural noun: ratios

    the quantitative relation between two amounts showing the number of times one value contains or is contained within the other.

That would seem to mean that two values widely different in magnitude would be considered to have a HIGH ratio. But if there is a big difference between the magnitude of signal and noise where the noise is much greater than the signal, we call it a LOW ratio.

--- End quote ---

You haven't been listening: if the signal is much lower than the noise, then the SNR is LOW. That's exactly what you said and is exactly the way it should be.

--- End quote ---

Yep, but his point seems to be that "ratio" shouldn't have an order. If we follow his reasoning above, he sees a "ratio" as the greater value over the lower value.
But a ratio is just a fraction, and order does matter.

But even if we just take the definition in a general dictionary (not even scientific or technical):

--- Quote ---ratio
noun, plural ra·tios.
the relation between two similar magnitudes with respect to the number of times the first contains the second
--- End quote ---

So even in the general definition, there is no ambiguity. The order of the two values is definitely part of the definition. :-//
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