 # 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

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

Where,

$$\begin{array}{l}P_{signal}\end{array}$$
is the power of a signal
$$\begin{array}{l}P_{noise}\end{array}$$
is the background noise

The signal to noise ratio formula is

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

Here,

$$\begin{array}{l}\sigma\end{array}$$
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:

$$\begin{array}{l}\mu =\frac{1+5+6+8+10}{5}=6\end{array}$$

Standard deviation of the data given:

$$\begin{array}{l}\sigma =\sqrt{\frac{1}{n-1}\sum_{t-1}^{2}\left(x_{1}-\mu\right)^{2}}\end{array}$$

$$\begin{array}{l}=\sqrt{\frac{1}{5-1}\left[(1-6)^{2}+(5-6)^{2}+(6-6)^{2}+(8-6)^{2}+(10-6)^{2}\right]} \\=\sqrt{\frac{46}{4}} \\=\sqrt{11.5} \\=3.39\end{array}$$

Then,

Signal to noise ratio = 6/3.39

Signal to Noise Ration =1.77