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## Main Question or Discussion Point

Hello everyone!

It seems to me that there are many ways of calculating SNR depending on the type of signal and the nature of problems. I was able to get a decent amount of information for electrical signals but couldn't find resources which discuss the topic in a more generalized manner. I was reading a research paper which calculates the SNR using the method mentioned below:

The signal here is simulating the Lorentzian curve of intensity measured by a spectrophotometer and the white noise is added randomly from a Gaussian distribution during the simulation. (Link to the paper:

It is unclear to me as to what the author implies with the above-mentioned statement. I get that you need to take the variance of the noise distribution, but the part where he says that the signal to be considered is the height with power normalised to 1 doesn't make complete sense to me. What goes in the numerator? Is it the height of the graph at it's peak? or perhaps the average of the height of the graph for the selected range of frequencies? Also, why are different people using different ways to calculate Signal to Noise Ratio? Most people seem to use the ratio of powers wherever both of these quantities are available, others use variances of the signal and the noise, and then there's this paper which uses the ratio of Intensity(?) of the signal to the variance of the noise. You can ask follow up questions if my message doesn't make sense. I am very new to evaluating performance of signals so I apologise if I get the technical jargon wrong somewhere during the conversation.

Have a nice day!

It seems to me that there are many ways of calculating SNR depending on the type of signal and the nature of problems. I was able to get a decent amount of information for electrical signals but couldn't find resources which discuss the topic in a more generalized manner. I was reading a research paper which calculates the SNR using the method mentioned below:

*"where the signal is defined as the height of the signal (power normalized to 1) and the noise is the variance of the noise distribution"*

The signal here is simulating the Lorentzian curve of intensity measured by a spectrophotometer and the white noise is added randomly from a Gaussian distribution during the simulation. (Link to the paper:

*https://www.osapublishing.org/oe/abstract.cfm?uri=oe-16-2-1020*: the part I am referring to can be found in the last paragraph of page 4 of the PDF version.)It is unclear to me as to what the author implies with the above-mentioned statement. I get that you need to take the variance of the noise distribution, but the part where he says that the signal to be considered is the height with power normalised to 1 doesn't make complete sense to me. What goes in the numerator? Is it the height of the graph at it's peak? or perhaps the average of the height of the graph for the selected range of frequencies? Also, why are different people using different ways to calculate Signal to Noise Ratio? Most people seem to use the ratio of powers wherever both of these quantities are available, others use variances of the signal and the noise, and then there's this paper which uses the ratio of Intensity(?) of the signal to the variance of the noise. You can ask follow up questions if my message doesn't make sense. I am very new to evaluating performance of signals so I apologise if I get the technical jargon wrong somewhere during the conversation.

Have a nice day!