# Signal to Noise Ratio Formula

Signal to noise ratio helps compute the value of a signal-to-noise, which informs us about the signal’s quality. It is abbreviated as S/N or SNR. It is noteworthy that such a ratio is a qualitative measure. The formula calculates the ratio of the intensity of the received signal to the strength of the disturbance in the transmitter.

It is often used to determine the quality of transmission. Simply put, it is the light signal to noise signal ratio. Often stated in decibels, a signal-to-noise ratio greater than 1:1 or more than 0 dB implies that the signal is stronger than the noise.

**Formula**

SNR = P_{signal}/P_{noise}=µ/σwhere

- P
_{signal}denotes the signal’s power, the population mean- P
_{noise}denotes the power of noise, the standard deviation of data

**Sample Problems**

**Question 1: Find the SNR of the data set: 1, 4, 7, 8, 10.**

**Solution:**

Mean = µ = (1+4+7+8+10)/5

= 30/5

= 6

Standard Deviation, σ = √((1 – 6)

^{2}+ (4 – 6)^{2}+ (7 – 6)^{2}+ (8 – 6)^{2}+ (10 – 6)^{2})/5= √((25 + 4 + 1 + 4 + 16)/5)

= √(50/4)

= 3.53

SNR = µ/σ

= 6/3.16

SNR = 1.89

**Question 2: Find the SNR of the following data set: 5, 9, 4, 2, 12.**

**Solution:**

Mean = µ = (5+9+4+2+12)/5

= 6.4

Standard Deviation, σ = √((5 – 6.4)

^{2}+ (9 – 6.4)^{2}+ (4 – 6.4)^{2}+ (2 – 6.4)^{2}+ (12 – 6.4)^{2})/5= √((1.96 + 6.76 + 5.76 + 19.36 + 31.36)/5)

= √(65.2/5)

= 3.61

SNR = µ/σ

= 6.4/3.61

SNR = 1.77

**Question 3: Find the SNR for the following data: 6, 24, 6, 14, 10.**

**Solution:**

Mean = µ = (6+24+6+14+10)/5

= 60/5

= 12

Standard Deviation, σ = √((6 – 12)

^{2}+ (24 – 12)^{2}+ (6 – 12)^{2}+ (14 – 12)^{2}+ (10 – 12)^{2})/5= √(36 + 144 + 36 + 4 + 4)/5)

= √(224/5)

= 6.69

SNR = µ/σ

= 12/6.69

SNR = 1.79

**Question 4: What would be the standard deviation of the data if the mean is 45 and SNR is 39.5?**

**Solution:**

Given: µ = 45 and SNR = 1.139

Since, SNR = µ/σ

⇒ σ = µ/SNR

= 45/1.139

σ = 39.5

**Question 5: Find the standard deviation of the data if the mean is 28 and SNR is 4.**

**Solution:**

Given: µ = 28 and SNR = 4

Since, SNR = µ/σ

⇒ σ = µ/SNR

= 28/4

σ = 7