Why report SNR, and what SNR is acceptable?

I see several papers that quantify animal sounds and include the SNR (signal-to-noise ratio) of the signals of interest. Why is this done - surely a signal wouldn't be detected if the SNR was insufficient (?)

Additionally, is there a rule-of-thumb on the minimum acceptable SNR of a given signal that acts as a threshold to whether or not you should extract parameters from to quanitfy in the first place?

SNR is relevant for detection and not for characterization of the sound. The only reason why someone may specify SNR is to indicate that the data are of good quality. Now, the question on what constitutes a sufficient SNR does not really depend on the signal but on the noise statistics.

For the (Neyman-Pearson) threshold detector one typically choses the threshold such that the probability of false alarm is below a given threshold. So, in detection theory, one studies the noise statistics and determines the necessary threshold accordingly.

Obviously, a detection threshold (minimal SNR) is useless if probability of false alarm is not given.

Edit: Any decision on the presence of a signal may be correct or false. The probability of detection is then the ratio of true positives to total number of detections and the probability of false alarm is the number of false alarms to total number of detections.

(begin rant: this is why I'm a little bit frustrated about replacing probability of detection and probability of false alarm by precision and recall; end rant)

• What would be the formula for probability of false alarm? #false alarms/total number detections? Jul 5, 2022 at 20:33
• I edited my answer
– WMXZ
Jul 6, 2022 at 4:25
• thanks that is helpful Jul 6, 2022 at 14:28
• Thanks for the edit. To clarify, in a binary problem (signal vs noise), your definition of probability of detection (ratio of true positives to total number of detections) sounds identical to precision, and probability of false alarms definition sounds the same as false discovery rate, I think (i.e., 1-precision). Is it correct that those are the same definitions? I don't see how probability of false alarm is being replaced by recall since recall is more about assessing false negatives. Apologies for my confusion, just want to make sure I'm not incorrectly conflating terminology! Jul 6, 2022 at 18:59
• The problem with the precision-recall curve is the use of precision, which is correlated with the abundance of the target signal. If the target signal is abundant, even a bad detector can achieve a high precision. Conversely, if the target signal is rare, precision can be low even with a very good detector. This shortcoming can be mitigated by using a statistic for reporting false positives that is less correlated with abundance, like number of false positives per unit time, which provides an estimate of type II error that is less confounded by the abundance of the target signal. Aug 14, 2022 at 23:23

I think it depends on your research question. I've used SNR in my study of the effects of noise on bottlenose dolphin whistle communication because I'm specifically interested in parameters such as min/max frequency, start/end frequency which can be effected by noise. I want to use an SNR threshold to ensure that observed shifts in the frequency content of whistles is due to changes to the whistle, not because of reduced detectability in high noise (i.e. missing the end of a faint whistle). Similar studies have more subjectively judged whether a full contour is present (visual categorisation into high/low quality, presence of harmonics) but I think use of an SNR threshold is more objective. If your question was more about presence/absence of a species then the SNR of the vocalisation might not matter, so long as it was detected.

For the example on bottlenose dolphin whistle communication used above, I apply a SNR threshold of 6dB (roughly twice the amplitude of the noise) but I don't think there's a one-size-fits-all answer to what threshold is broadly applicable.

• I agree, I use SNR to pre-filter recordings before I analyze them for acoustic structure metrics, which can be affected by background noise and therefore bias your measurements. Jul 6, 2022 at 16:00

In this paper we evaluated the effect of background noise (measured as SNR) on the precision of several metrics of acoustic structure, like cross-correlation, spectral and spectrographic parameters and dynamic-time warping. Long story short, most metrics behaved well under low SNR values (2 dB) and pretty much all remained pretty consistent above 6 dB SNR.

Reference

Araya-Salas, M., Smith-Vidaurre, G., & Webster, M. (2019). Assessing the effect of sound file compression and background noise on measures of acoustic signal structure. Bioacoustics, 28(1), 57-73.

SNR can be used/provided for a variety of different reasons. However, for the characterization of a signals property, the signal to noise ratio may or may not be important as you can always do an estimated removal of background noise from the signal before characterizing its properties. However, this removal of background noise will have a minimal effect on the signal properties unless the SNR is quite low, i.e. approaching masking of the signal, as generally the subtraction of background noise in the units of uPa^2 is often negligible in these circumstances. There is no rule of thumb of an appropriate SNR that I am aware of, but you would want the signal to be well above background noise across its frequency composition to ensure that things like PSD reflect the signal and not the noise. Perhaps 6dB or higher would be appropriate. So while that is important, it is also important that the characterization of a signals is based upon signals that have not been subjected to high transmission loss across its spectral components. For example, if you were characterizing a signal, you would ideally like that its frequency composition be present so you can get a good picture of its actual PSD, etc. So I would say that SNR and signal amplitude are both important to ensure the results portray the actual signal vs. noise and impacts from varying levels of transmission loss as a function of the signal's frequency composition.

Lastly, for detection and presence data, it is often useful to provide an estimate of the SNR required for a signal to be detected. This is true for both automated detectors and manual review. For manual review of spectrograms, etc., different people require different SNRs of signals to "see" them amongst background noise. As background noise changes often as a function of time, if SNRs of detection are static then this change in noise levels effectively changes the sampling range of a sensor. It can get complicated, but it is something to consider when analyzing results.

There is also this paper which discusses SNR & its relation to acoustic measurements -

High microphone signal-to-noise ratio enhances acoustic sampling of wildlife