Signal to noise ratio semantics - Page 1
Forum section: electronics / general

author: Circlotron
author_rank: Super Contributor
timestamp: August 30, 2022, 03:12:13 am
content: When two quantities are compared, AFAICT if their values differ greatly then there is a high ratio between them. If their values are closer to each other then there is a low ratio. If that is the case (and maybe it isn't?) then why if a signal is very weak in a noisy environment so that the relative strengths of each differ greatly, is that considered to be a LOW s/n ratio? Why not a high ratio? Or for that matter, with a car gearbox when the input shaft rotates several times for the output shaft to rotate once we say it has a LOW ratio, but the numeric ratio is relatively great compared to top gear. I know it's just semantics but there must be some history in this.

author: Brumby
author_rank: Unknown
timestamp: August 30, 2022, 04:19:22 am
content: It's in the terminology: Signal to Noise. We're interested in the amount of signal and if that's down compared to the noise, we call it low.If you want it the other way around, then use Noise to Signal.JMO

author: Circlotron
author_rank: Super Contributor
timestamp: August 30, 2022, 04:29:03 am
content: Quote from: Brumby on August 30, 2022, 04:19:22 amIf the terminology was "signal to noise" then yes, I agree.But if the terminology is "signal to noiseratio" that's when the confusion starts.

author: SiliconWizard
author_rank: Super Contributor
timestamp: August 30, 2022, 04:31:44 am
content: I don't understand where the confusion comes from. Possibly we are missing something.Signal-to-noise ratio = ratio of signal over noise = amplitude of signal / amplitude of noise.

author: Brumby
author_rank: Unknown
timestamp: August 30, 2022, 04:48:06 am
content: I don't see the confusion either. By definition, the order of the two components is clear. It's the ratio of signal to noise. Simple.There's nothing mysterious about the term ratio. It is exactly what it says. Whether gears are 10:1 or 1:10 is clarified by the descriptor. The descriptor here is specified every time you use such a reference:SignaltoNoise.Say you have a signal that +5dBm and noise of -5dBm, the SNR is +10dBIf you have a signal that -5dBm and noise of +5dBm, the SNR is -10dBIf you want the inverse of Noise to Signal, then example 1 is -10dB and example 2 is +10dB. That would be confusing.

author: Circlotron
author_rank: Super Contributor
timestamp: August 30, 2022, 05:26:17 am
content: The confusion stems from the terms LOW and HIGH.noun: ratio; plural noun: ratiosthe quantitative relation between two amounts showing thenumber of timesone 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.

author: fourfathom
author_rank: Super Contributor
timestamp: August 30, 2022, 05:47:02 am
content: Quote from: Circlotron on August 30, 2022, 05:26:17 amPerhaps it's because when signal < noise then the ratio is a negative number. We usually consider negative to be lower than positive.

author: eugene
author_rank: Frequent Contributor
timestamp: August 30, 2022, 12:52:02 pm
content: Quote from: Circlotron on August 30, 2022, 05:26:17 amYou 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.

author: alm
author_rank: Super Contributor
timestamp: August 30, 2022, 01:19:06 pm
content: Maybe it helps to talk about voltage ratios rather than ratios of decibels? If you have a 10 mVrms signal and 1 mVrms noise, the signal to noise ratio is 10. While a 1 mVrms signal with 10 mVrms noise has a snr of 0.1, a much smaller number. A stronger signal of 100 mV with 1 mV noise gives a signal to noise ratio of 100, an even higher number.

author: TimFox
author_rank: Super Contributor
timestamp: August 30, 2022, 03:50:00 pm
content: Since signal power (or rms voltage) and noise power (or rms noise voltage) are, by definition, positive-definite quantities, their ratio can never be negative.When the signal power is less than the noise power, then the signal/noise ratio is a positive value, less than one.When translated into dB, a ratio <1 is a negative dB value.In mathematical notation, a ratio can be written as A/B or A:B, which have identical meanings.An archaic mathematical notation is A:B::C:D, which means A/B = C/D.In English, that can be read as "A to B" or "the ratio of A to B".

author: ejeffrey
author_rank: Super Contributor
timestamp: August 30, 2022, 04:54:06 pm
content: 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.

author: fourfathom
author_rank: Super Contributor
timestamp: August 30, 2022, 05:11:23 pm
content: Quote from: TimFox on August 30, 2022, 03:50:00 pmThis 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.

author: SiliconWizard
author_rank: Super Contributor
timestamp: August 30, 2022, 08:08:30 pm
content: Quote from: eugene on August 30, 2022, 12:52:02 pmYep, 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):QuoteSo even in the general definition, there is no ambiguity. The order of the two values is definitely part of the definition.