Signal to Noise Ratio Formula

To detect the quality of a signal, the signal to noise ratio term is used. Simply, it is the ratio of the light signal to the noise signal. Often expressed in decibels, a ratio when is higher than 1: 1, or greater than 0 dB, indicates that the signal is more compared to noise.

Signal to noise ratio is often written as S/N or SNR. In Digital sense, this ratio refers useful information, false information, spam or the things that are off-topic or unrelated to the webpage, often regarded as “noise” and how the noise interferes with “signal” made to apt discussions.

The ratio is given as

$$SNR=\frac{P_{signal}}{P_{noise}}$$

Where,

 is the power of a signal

$\begin{array}{l}{P}_{noise}\end{array}$

is the background noise

The signal to noise ratio formula is

$$SNR=\frac{\mu }{\sigma }$$

Here,

is the standard deviation

$\begin{array}{l}\mu \end{array}$

 is the mean of the given data

Solved example

Question:  Determine the signal to noise ratio for the following data: 1, 5, 6, 8, 10.

Solution:

Find out the mean:

Standard deviation of the data given:

Then,

Signal to noise ratio = 6/3.39

Signal to Noise Ration =1.77