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Signal to Noise Ratio Calculator
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Signal to noise calculator is an online statistical calculator used to find out the ratio between the signal and noise. It is easy to calculate if we provide the mean and standard deviation of any observation. The equation for the particular calculation is given below.

SNR=$\frac{p_{signal}}{p_{noise}}$=$\frac{\mu }{\sigma }$

Where SNR is the signal to noise ratio
$p_{signal}$ is the signal power
$p_{noise}$ is the background noise
$\mu$ is the mean
$\sigma$ is the standard deviation

## Steps for Signal to Noise Ratio Calculator

Step 1 :

Note down the given observations.

Step 2 :

Find out the mean of the data using the following equation.

$\mu$ =$\frac{x_{1}+x_{2}+.......+x_{n}}{n}$

Step 3 :

Calculate the standard deviation using the formula,

S=$\sqrt{\frac{1}{n-1}\sum_{i=1}^{n}(x_{i}-\mu )^{2}}$

Step 4 :

Signal to noise ratio is given by,

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

## Problems on Signal to Noise Ratio Calculator

1. ### Determine the signal to noise ratio of the following observations.3,5,7,9

Step 1 :

The given observations are,

3,5,7,9

Step 2 :

Mean $\mu$ is given by,

$\mu$ =$\frac{x_{1}+x_{2}+.......+x_{n}}{n}$

$\mu$ =$\frac{3+5+7+9}{4}$

$\mu$ =$\frac{24}{4}$=6

Step 3 :

Standard deviation is given as,

S=$\sqrt{\frac{1}{n-1}\sum_{i=1}^{n}(x_{i}-\mu )^{2}}$

$\sum_{i=1}^{n}(x_{i}-\mu )^{2}$=(3-6)2+(5-6)2+(7-6)2+(9-6)2

$\sum_{i=1}^{n}(x_{i}-\mu )^{2}$=9+1+1+9=20

S=$\sqrt{\frac{1}{4-1}×20}$=2.5819

Step 4 :

Signal noise ration,

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

SNR= $\frac{6}{2.5819}$ = 2.3237

SNR=2.3237

2. ### Calculate the signal to noise ratio if the data is given as 10,20,30?

Step 1 :

The given observations are,

10,20,30

Step 2 :

Mean $\mu$ is given by,

$\mu$ =$\frac{x_{1}+x_{2}+.......+x_{n}}{n}$

$\mu$ =$\frac{10+20+30}{3}$

$\mu$ =$\frac{60}{3}$=20

Step 3 :

Sample standard deviation is

S=$\sqrt{\frac{1}{n-1}\sum_{i=1}^{n}(x_{i}-\mu )^{2}}$

$\sum_{i=1}^{n}(x_{i}-\mu )^{2}$=(10-20)2+(20-20)2+(30-20)2

$\sum_{i=1}^{n}(x_{i}-\mu )^{2}$=100+100=200

S=$\sqrt{\frac{1}{3-1}×200}$=10

Step 4 :

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

SNR=$\frac{20}{10}$=2