# Definition of NMR peak

In NMR a spectrum consists of noise and peaks. While steps, such as repeated scans or smoothing of the spectra can reduce noise some still remains. As such one step usually taken is to bin the data so that only peaks are chosen, usually with a threshold and finding maxima/minima. This raises the question however, which is how do you define a peak. If you use a threshold a poor baseline can result in this failing, for instance if the baseline is above the threshold set.

Is there a widely used method/rule of thumb which is used to decide if a region contains a peak, or is just noise?

• What helps in NMR is that for signals originating from a given molecule, the number of hydrogen atoms is an integer, and so signal strengths (integrals) should be approximately ratios of (fairly small) integers. If you have a couple of signals well above the signal to noise level, chances are that all signals originating from that molecule should be above the noise level (unless some signals are broadened significantly). – Karsten Theis Nov 11 '19 at 15:22
• If your standard 1D spectrum still has a distorted baseline after zeroth and first order phase correction, something was wrong with the measurement. Unfortunately your "experts" at hand may very well not be aware of the problem, which can be any of a dozen. – Karl Nov 11 '19 at 21:15

A general term used in all analytical chemistry is the lower limit of detection (LoD), which is generally defined as 3 times the standard deviation of the baseline/blank. So if you calculate the $$\sigma$$ standard deviation of the baseline in question, and you have a signal that is over $$3 \sigma$$, you can generally accept that as a peak. This comes down to the so-called 68-95-99.7 rule, according to which there is only a 0.3% probability that a peak higher than the LoD is an artifact.