# Confused about the Signal to Noise Ratio

• otaKu
In summary: This is usually expressed in decibels by taking 10 times the log of the square of the amplitudes.In summary, the concept of signal-to-noise ratio (SNR) has multiple definitions depending on the context and application. It can refer to power or amplitude and is often expressed in decibels. The numerator represents the amplitude or power of the signal of interest, while the denominator represents the amplitude or power of the noise. Normalized amplitude is defined by assigning a value of 1 to the maximum amplitude and expressing other values as a multiplier of this normalized value. SNR is commonly used to evaluate the performance of signals, but its calculation may vary based on the specific needs of the application.

#### otaKu

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:

"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!

There is no single definition of SNR; it depends in the context.

Your SNR is equal to 1 when the level of you signal (whatever that is) is equal to the level of your noise (whatever is causing the noise). The signal could be voltage, power, intensity, length, frequency etc (just to mention a few I come across in my work).
This is -as far as I am aware about as close to a "general" definition as you can get. There are of course lots of different definitions of the SNR for specific applications and in some context there is indeed just one -widely accepted- definition, but generally speaking you need to look at the formula used to see what is meant.

The signal is the part you are interested in. The noise is everything else. Therefore, it is subjective.

otaKu said:
the height with power normalised to 1 doesn't make complete sense to me. What goes in the numerator?
The numerator is the amplitude of the signal you are interested in,
The denominator is the amplitude of the noise.
"Amplitude", as @f95toli noted, can be any of various measurements.
SNR is frequently expressed in decibels (db), which is 10 times the logarithm of the fraction calculated above.

A 'normalized' amplitude is defined by assigning a value of "1" to the maximum amplitude, then expressing related values as a multiplier (which may be less than or more than 1) of the normalized value.

Hope this helps!

Cheers,
Tom

Tom.G said:
The numerator is the amplitude of the signal you are interested in,
The denominator is the amplitude of the noise.
"Amplitude", as @f95toli noted, can be any of various measurements.
SNR is frequently expressed in decibels (db), which is 10 times the logarithm of the fraction calculated above.

A 'normalized' amplitude is defined by assigning a value of "1" to the maximum amplitude, then expressing related values as a multiplier (which may be less than or more than 1) of the normalized value.

Hope this helps!

Cheers,
Tom
Signal to Noise ratio, by convention, refers to power, not amplitude, so the ratio in decibels will be 10 times the log of the power ratio. The power definition removes any issue about the wave shape.
If we use amplitude, there is a problem when the noise is statistical and the signal is sinusoidal. (In any case, for amplitude we need to take 20 times the log of the amplitudes, not 10 times).
With amplitude, there is also a complication where the signal source is not matched to a noisy receiver, because the decibel definition for amplitudes presumes equal impedances,.
It is also common to really mean Signal+Noise / Noise ration, as a pure signal is not usually obtainable in practice.

## 1. What is the Signal to Noise Ratio (SNR) in scientific research?

The Signal to Noise Ratio is a measure of the strength of a signal compared to the level of background noise. In scientific research, it is used to determine the quality or reliability of data obtained from experiments or measurements.

## 2. Why is the SNR important in scientific research?

The SNR is important because it helps scientists distinguish between the signal, which is the desired information, and the noise, which is unwanted or irrelevant information. A high SNR indicates a strong signal and low levels of noise, which leads to more accurate and reliable results.

## 3. How is the SNR calculated?

The SNR is calculated by dividing the amplitude of the signal by the standard deviation of the noise. This can be expressed mathematically as SNR = A/σ, where A is the amplitude of the signal and σ is the standard deviation of the noise.

## 4. What factors can affect the SNR?

The SNR can be affected by various factors, including the sensitivity of the measuring instrument, the quality of the signal source, the level of background noise, and the distance between the signal source and the measuring instrument. Environmental factors such as temperature and electromagnetic interference can also impact the SNR.

## 5. How can scientists improve the SNR in their experiments?

To improve the SNR in experiments, scientists can use high-quality equipment, reduce sources of noise, and increase the strength of the signal being measured. They can also use signal processing techniques such as filtering and averaging to enhance the signal and reduce noise. Proper experimental design and careful data analysis can also help improve the SNR.