Sign to-commotion proportion (contracted SNR) is a measure utilized as a part of science and designing that analyzes the level of a coveted sign to the level of foundation clamor. It is characterized as the proportion of sign energy to the clamor power, regularly communicated in decibels. A proportion higher than 1:1 (more prominent than 0 dB) shows more flag than clamor. While SNR is regularly cited for electrical signs, it can be connected to any type of sign, (for example, isotope levels in an ice center or biochemical motioning between cells).

Signal-to-noise ratio is defined as the ratio of the power of a signal (meaningful information) and the power of background noise (unwanted signal):

If the variance of the signal and noise are known, and the signal is zero:

If the signal and the noise are measured across the same impedance, then the SNR can be obtained by calculating the square of the amplitude ratio:

Where A is root mean square (RMS) amplitude (for example, RMS voltage).

## Decibels

Because many signals have a very wide dynamic range, signals are often expressed using the logarithmic decibel scale. Based upon the definition of decibel, signal and noise may be expressed in decibels (dB) as

and

In a similar manner, SNR may be expressed in decibels as

Using the definition of SNR

Using the quotient rule for logarithms

Substituting the definitions of SNR, signal, and noise in decibels into the above equation results in an important formula for calculating the signal to noise ratio in decibels, when the signal and noise are also in decibels:

In the above formula, P is measured in units of power, such as Watts or mill watts, and signal-to-noise ratio is a pure number.

However, when the signal and noise are measured in Volts or Amperes, which are measures of amplitudes, they must be squared to be proportionate to power as shown below:

= 20log_{10}(\frac{A_{signal}}{A_{noise}}) \\[7pt]

= A_{signal,dB} – A_{noise,dB}} $

### Example

**Problem Statement:**

Compute the SNR of a 2.5 kHz sinusoid sampled at 48 kHz. Add white noise with standard deviation 0.001. Set the random number generator to the default settings for reproducible results.

**Solution:**

x = sin(2 \times pi \times \frac{F_i}{F_s} \times (1:N)) + 0.001 \times randn(1,N); \\[7pt]

SNR = snr(x,Fs) \\[7pt]

SNR = 57.7103}$

Table of Contents

1.statistics adjusted rsquared

2.statistics analysis of variance

4.statistics arithmetic median

8.statistics best point estimation

9.statistics beta distribution

10.statistics binomial distribution

11.statistics blackscholes model

13.statistics central limit theorem

14.statistics chebyshevs theorem

15.statistics chisquared distribution

16.statistics chi squared table

17.statistics circular permutation

18.statistics cluster sampling

19.statistics cohens kappa coefficient

21.statistics combination with replacement

23.statistics continuous uniform distribution

24.statistics cumulative frequency

25.statistics coefficient of variation

26.statistics correlation coefficient

27.statistics cumulative plots

28.statistics cumulative poisson distribution

30.statistics data collection questionaire designing

31.statistics data collection observation

32.statistics data collection case study method

34.statistics deciles statistics

36.statistics exponential distribution

40.statistics frequency distribution

41.statistics gamma distribution

43.statistics geometric probability distribution

46.statistics gumbel distribution

49.statistics harmonic resonance frequency

51.statistics hypergeometric distribution

52.statistics hypothesis testing

53.statistics interval estimation

54.statistics inverse gamma distribution

55.statistics kolmogorov smirnov test

57.statistics laplace distribution

58.statistics linear regression

59.statistics log gamma distribution

60.statistics logistic regression

63.statistics means difference

64.statistics multinomial distribution

65.statistics negative binomial distribution

66.statistics normal distribution

67.statistics odd and even permutation

68.statistics one proportion z test

69.statistics outlier function

71.statistics permutation with replacement

73.statistics poisson distribution

74.statistics pooled variance r

75.statistics power calculator

77.statistics probability additive theorem

78.statistics probability multiplicative theorem

79.statistics probability bayes theorem

80.statistics probability density function

81.statistics process capability cp amp process performance pp

83.statistics quadratic regression equation

84.statistics qualitative data vs quantitative data

85.statistics quartile deviation

86.statistics range rule of thumb

87.statistics rayleigh distribution

88.statistics regression intercept confidence interval

89.statistics relative standard deviation

90.statistics reliability coefficient

91.statistics required sample size

92.statistics residual analysis

93.statistics residual sum of squares

94.statistics root mean square

96.statistics sampling methods

98.statistics shannon wiener diversity index

99.statistics signal to noise ratio

100.statistics simple random sampling

102.statistics standard deviation

103.statistics standard error se

104.statistics standard normal table

105.statistics statistical significance

108.statistics stem and leaf plot

109.statistics stratified sampling

112.statistics tdistribution table

113.statistics ti 83 exponential regression

114.statistics transformations

116.statistics type i amp ii errors

119.statistics weak law of large numbers