Signal - to - noise ratio - wikipedia Signal - to - noise ratio For `` signal - to - noise ratio '' in statistics, see Effect size. For other uses, see Signal to Noise ( disambiguation ). Signal - to - noise ratio ( abbreviated SNR or S / N ) is a measure used in science and engineering that compares the level of a desired signal to the level of background noise. SNR is defined as the ratio of signal power to the noise power, often expressed in decibels. A ratio higher than 1 : 1 ( greater than 0 dB ) indicates more signal than noise. While SNR is commonly quoted for electrical signals, it can be applied to any form of signal for example isotope levels in an ice core or biochemical signaling between cells or financial trading signals. Signal - to - noise ratio is sometimes used metaphorically to refer to the ratio of useful information to false or irrelevant data in a conversation or exchange. For example, in online discussion forums and other online communities, off - topic posts and spam are regarded as `` noise '' that interferes with the `` signal '' of appropriate discussion. The signal - to - noise ratio, the bandwidth, and the channel capacity of a communication channel are connected by the Shannon -- Hartley theorem. Contents 1 Definition 1.1 Decibels 1.2 Dynamic range 1.3 Difference from conventional power 2 Alternative definition 3 SNR for various modulation systems 3.1 Amplitude modulation 3.2 Frequency modulation 4 Improving SNR in practice 5 Digital signals 5.1 Fixed point 5.2 Floating point 6 Optical SNR 7 Types and abbreviations 8 See also 9 Notes 10 References 11 External links Definition Signal - to - noise ratio is defined as the ratio of the power of a signal ( meaningful information ) to the power of background noise ( unwanted signal ) : S N R = P s i g n a l P n o i s e, ( displaystyle mathrm ( SNR ) = ( \frac ( P_ ( mathrm ( signal ) ) ) ( P_ ( mathrm ( noise ) ) ) ), ) where P is average power. Both signal and noise power must be measured at the same or equivalent points in a system, and within the same system bandwidth. If the variance of the signal and noise are known, and the signal and noise are both zero - mean, SNR can be : S N R = σ s i g n a l 2 σ n o i s e 2. ( displaystyle mathrm ( SNR ) = ( \frac ( sigma _ ( mathrm ( signal ) ) ^ ( 2 ) ) ( sigma _ ( mathrm ( noise ) ) ^ ( 2 ) ) ). ) If the signal and the noise are measured across the same impedance, the SNR can be obtained by calculating the square of the amplitude ratio : S N R = P s i g n a l P n o i s e = ( A s i g n a l A n o i s e ) 2, ( displaystyle mathrm ( SNR ) = ( \frac ( P_ ( mathrm ( signal ) ) ) ( P_ ( mathrm ( noise ) ) ) ) = left ( ( \frac ( A_ ( mathrm ( signal ) ) ) ( A_ ( mathrm ( noise ) ) ) ) \right ) ^ ( 2 ), ) 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 P s i g n a l, d B = 10 log 10 ⁡ ( P s i g n a l ) ( displaystyle P_ ( mathrm ( signal, dB ) ) = 10 log _ ( 10 ) left ( P_ ( mathrm ( signal ) ) \right ) ) and P n o i s e, d B = 10 log 10 ⁡ ( P n o i s e ). ( displaystyle P_ ( mathrm ( noise, dB ) ) = 10 log _ ( 10 ) left ( P_ ( mathrm ( noise ) ) \right ). ) In a similar manner, SNR may be expressed in decibels as S N R d B = 10 log 10 ⁡ ( S N R ). ( displaystyle mathrm ( SNR_ ( dB ) ) = 10 log _ ( 10 ) left ( mathrm ( SNR ) \right ). ) Using the definition of SNR S N R d B = 10 log 10 ⁡ ( P s i g n a l P n o i s e ). ( displaystyle mathrm ( SNR_ ( dB ) ) = 10 log _ ( 10 ) left ( ( \frac ( P_ ( mathrm ( signal ) ) ) ( P_ ( mathrm ( noise ) ) ) ) \right ). ) Using the quotient rule for logarithms 10 log 10 ⁡ ( P s i g n a l P n o i s e ) = 10 log 10 ⁡ ( P s i g n a l ) − 10 log 10 ⁡ ( P n o i s e ). ( displaystyle 10 log _ ( 10 ) left ( ( \frac ( P_ ( mathrm ( signal ) ) ) ( P_ ( mathrm ( noise ) ) ) ) \right ) = 10 log _ ( 10 ) left ( P_ ( mathrm ( signal ) ) \right ) - 10 log _ ( 10 ) left ( P_ ( mathrm ( noise ) ) \right ). ) 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 : S N R d B = P s i g n a l, d B − P n o i s e, d B. ( displaystyle mathrm ( SNR_ ( dB ) ) = ( P_ ( mathrm ( signal, dB ) ) - P_ ( mathrm ( noise, dB ) ) ). ) In the above formula, P is measured in units of power, such as Watts or miliWatts, 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 proportional to power as shown below : S N R d B = 10 log 10 ⁡ ( ( A s i g n a l A n o i s e ) 2 ) = 20 log 10 ⁡ ( A s i g n a l A n o i s e ) = ( A s i g n a l, d B − A n o i s e, d B ). ( displaystyle mathrm ( SNR_ ( dB ) ) = 10 log _ ( 10 ) left ( left ( ( \frac ( A_ ( mathrm ( signal ) ) ) ( A_ ( mathrm ( noise ) ) ) ) \right ) ^ ( 2 ) \right ) = 20 log _ ( 10 ) left ( ( \frac ( A_ ( mathrm ( signal ) ) ) ( A_ ( mathrm ( noise ) ) ) ) \right ) = left ( ( A_ ( mathrm ( signal, dB ) ) - A_ ( mathrm ( noise, dB ) ) ) \right ). ) Dynamic range The concepts of signal - to - noise ratio and dynamic range are closely related. Dynamic range measures the ratio between the strongest un-distorted signal on a channel and the minimum discernible signal, which for most purposes is the noise level. SNR measures the ratio between an arbitrary signal level ( not necessarily the most powerful signal possible ) and noise. Measuring signal - to - noise ratios requires the selection of a representative or reference signal. In audio engineering, the reference signal is usually a sine wave at a standardized nominal or alignment level, such as 1 kHz at + 4 dBu ( 1.228 V ). SNR is usually taken to indicate an average signal - to - noise ratio, as it is possible that ( near ) instantaneous signal - to - noise ratios will be considerably different. The concept can be understood as normalizing the noise level to 1 ( 0 dB ) and measuring how far the signal ' stands out '. Difference from conventional power In physics, the average power of an AC signal is defined as the average value of voltage times current ; for resistive ( non-reactive ) circuits, where voltage and current are in phase, this is equivalent to the product of the rms voltage and current : P = V r m s I r m s ( displaystyle mathrm ( P ) = V_ ( mathrm ( rms ) ) I_ ( mathrm ( rms ) ) ) P = V r m s 2 R = I r m s 2 R ( displaystyle mathrm ( P ) = ( \frac ( V_ ( mathrm ( rms ) ) ^ ( 2 ) ) ( R ) ) = I_ ( mathrm ( rms ) ) ^ ( 2 ) R ) But in signal processing and communication, one usually assumes that R = 1 Ω ( displaystyle R = 1 Omega ) so that factor is usually not included while measuring power or energy of a signal. This may cause some confusion among readers, but the resistance factor is not significant for typical operations performed in signal processing, or for computing power ratios. For most cases, the power of a signal would be considered to be simply P = V r m s 2 = A 2 2 ( displaystyle mathrm ( P ) = V_ ( mathrm ( rms ) ) ^ ( 2 ) = ( \frac ( A ^ ( 2 ) ) ( 2 ) ) ) where ' A ' is the amplitude of the AC signal. Alternative definition An alternative definition of SNR is as the reciprocal of the coefficient of variation, i.e., the ratio of mean to standard deviation of a signal or measurement : S N R = μ σ ( displaystyle mathrm ( SNR ) = ( \frac ( mu ) ( sigma ) ) ) where μ ( displaystyle mu ) is the signal mean or expected value and σ ( displaystyle sigma ) is the standard deviation of the noise, or an estimate thereof. Notice that such an alternative definition is only useful for variables that are always non-negative ( such as photon counts and luminance ). Thus it is commonly used in image processing, where the SNR of an image is usually calculated as the ratio of the mean pixel value to the standard deviation of the pixel values over a given neighborhood. Sometimes SNR is defined as the square of the alternative definition above. The Rose criterion ( named after Albert Rose ) states that an SNR of at least 5 is needed to be able to distinguish image features at 100 % certainty. An SNR less than 5 means less than 100 % certainty in identifying image details. Yet another alternative, very specific and distinct definition of SNR is employed to characterize sensitivity of imaging systems ; see Signal - to - noise ratio ( imaging ). Related measures are the `` contrast ratio '' and the `` contrast - to - noise ratio ''. SNR for various modulation systems Amplitude modulation Channel signal - to - noise ratio is given by ( S N R ) C, A M = A C 2 ( 1 + k a 2 P ) 2 W N 0 ( displaystyle mathrm ( ( SNR ) _ ( C, AM ) ) = ( \frac ( A_ ( C ) ^ ( 2 ) ( 1 + k_ ( a ) ^ ( 2 ) P ) ) ( 2WN_ ( 0 ) ) ) ) where W is the bandwidth and k a ( displaystyle k_ ( a ) ) is modulation index Output signal - to - noise ratio ( of AM receiver ) is given by ( S N R ) O, A M = A c 2 k a 2 P 2 W N 0 ( displaystyle mathrm ( ( SNR ) _ ( O, AM ) ) = ( \frac ( A_ ( c ) ^ ( 2 ) k_ ( a ) ^ ( 2 ) P ) ( 2WN_ ( 0 ) ) ) ) Frequency modulation Channel signal - to - noise ratio is given by ( S N R ) C, F M = A c 2 2 W N 0 ( displaystyle mathrm ( ( SNR ) _ ( C, FM ) ) = ( \frac ( A_ ( c ) ^ ( 2 ) ) ( 2WN_ ( 0 ) ) ) ) Output signal - to - noise ratio is given by ( S N R ) O, F M = A c 2 k f 2 P 2 N 0 W 3 ( displaystyle mathrm ( ( SNR ) _ ( O, FM ) ) = ( \frac ( A_ ( c ) ^ ( 2 ) k_ ( f ) ^ ( 2 ) P ) ( 2N_ ( 0 ) W ^ ( 3 ) ) ) ) Improving SNR in Practice Recording of the noise of a thermogravimetric analysis device that is poorly isolated from a mechanical point of view ; the middle of the curve shows a lower noise, due to a lesser surrounding human activity at night. All real measurements are disturbed by noise. This includes electronic noise, but can also include external events that affect the measured phenomenon -- wind, vibrations, gravitational attraction of the moon, variations of temperature, variations of humidity, etc., depending on what is measured and of the sensitivity of the device. It is often possible to reduce the noise by controlling the environment. Otherwise, when the characteristics of the noise are known and are different from the signals, it is possible to filter it or to process the signal. For example, it is sometimes possible to use a lock - in amplifier to modulate and confine the signal within a very narrow bandwidth and then filter the detected signal to the narrow band where it resides, thereby eliminating most of the broadband noise. When the signal is constant or periodic and the noise is random, it is possible to enhance the SNR by averaging the measurement. In this case the noise goes down as the square root of the number of averaged samples. Additionally, internal noise of electronic systems can be reduced by low - noise amplifiers. Digital signals When a measurement is digitized, the number of bits used to represent the measurement determines the maximum possible signal - to - noise ratio. This is because the minimum possible noise level is the error caused by the quantization of the signal, sometimes called Quantization noise. This noise level is non-linear and signal - dependent ; different calculations exist for different signal models. Quantization noise is modeled as an analog error signal summed with the signal before quantization ( `` additive noise '' ). This theoretical maximum SNR assumes a perfect input signal. If the input signal is already noisy ( as is usually the case ), the signal 's noise may be larger than the quantization noise. Real analog - to - digital converters also have other sources of noise that further decrease the SNR compared to the theoretical maximum from the idealized quantization noise, including the intentional addition of dither. Although noise levels in a digital system can be expressed using SNR, it is more common to use E / N, the energy per bit per noise power spectral density. The modulation error ratio ( MER ) is a measure of the SNR in a digitally modulated signal. Fixed point See also : Fixed point arithmetic For n - bit integers with equal distance between quantization levels ( uniform quantization ) the dynamic range ( DR ) is also determined. Assuming a uniform distribution of input signal values, the quantization noise is a uniformly distributed random signal with a peak - to - peak amplitude of one quantization level, making the amplitude ratio 2 / 1. The formula is then : D R d B = S N R d B = 20 log 10 ⁡ ( 2 n ) ≈ 6.02 ⋅ n ( displaystyle mathrm ( DR_ ( dB ) ) = mathrm ( SNR_ ( dB ) ) = 20 log _ ( 10 ) ( 2 ^ ( n ) ) approx 6.02 cdot n ) This relationship is the origin of statements like `` 16 - bit audio has a dynamic range of 96 dB ''. Each extra quantization bit increases the dynamic range by roughly 6 dB. Assuming a full - scale sine wave signal ( that is, the quantizer is designed such that it has the same minimum and maximum values as the input signal ), the quantization noise approximates a sawtooth wave with peak - to - peak amplitude of one quantization level and uniform distribution. In this case, the SNR is approximately S N R d B ≈ 20 log 10 ⁡ ( 2 n 3 / 2 ) ≈ 6.02 ⋅ n + 1.761 ( displaystyle mathrm ( SNR_ ( dB ) ) approx 20 log _ ( 10 ) ( 2 ^ ( n ) ( sqrt ( 3 / 2 ) ) ) approx 6.02 cdot n + 1.761 ) Floating point Floating - point numbers provide a way to trade off signal - to - noise ratio for an increase in dynamic range. For n bit floating - point numbers, with n-m bits in the mantissa and m bits in the exponent : D R d B = 6.02 ⋅ 2 m ( displaystyle mathrm ( DR_ ( dB ) ) = 6.02 cdot 2 ^ ( m ) ) S N R d B = 6.02 ⋅ ( n − m ) ( displaystyle mathrm ( SNR_ ( dB ) ) = 6.02 cdot ( n-m ) ) Note that the dynamic range is much larger than fixed - point, but at a cost of a worse signal - to - noise ratio. This makes floating - point preferable in situations where the dynamic range is large or unpredictable. Fixed - point 's simpler implementations can be used with no signal quality disadvantage in systems where dynamic range is less than 6.02 m. The very large dynamic range of floating - point can be a disadvantage, since it requires more forethought in designing algorithms. Optical SNR Optical signals have a carrier frequency that is much higher than the modulation frequency ( about 200 THz and more ). This way the noise covers a bandwidth that is much wider than the signal itself. The resulting signal influence relies mainly on the filtering of the noise. To describe the signal quality without taking the receiver into account, the optical SNR ( OSNR ) is used. The OSNR is the ratio between the signal power and the noise power in a given bandwidth. Most commonly a reference bandwidth of 0.1 nm is used. This bandwidth is independent of the modulation format, the frequency and the receiver. For instance an OSNR of 20 dB / 0.1 nm could be given, even the signal of 40 GBit DPSK would not fit in this bandwidth. OSNR is measured with an optical spectrum analyzer. Types and abbreviations Signal to noise ratio may be abbreviated as SNR and less commonly as S / N. PSNR stands for Peak signal - to - noise ratio. GSNR stands for Geometric Signal - to - Noise Ratio. SINR is the Signal - to - noise - plus - interference ratio. See also Audio system measurements Generation loss Matched filter Near - far problem Noise margin Omega ratio Peak signal - to - noise ratio Signal - to - noise statistic Signal - to - noise - plus - interference ratio Signal to noise ratio ( imaging ) SINAD Subjective video quality Total harmonic distortion Video quality Notes Jump up ^ The connection between optical power and voltage in an imaging system is linear. This usually means that the SNR of the electrical signal is calculated by the 10 log rule. With an interferometric system, however, where interest lies in the signal from one arm only, the field of the electromagnetic wave is proportional to the voltage ( assuming that the intensity in the second, the reference arm is constant ). Therefore the optical power of the measurement arm is directly proportional to the electrical power and electrical signals from optical interferometry are following the 20 log rule. Jump up ^ The exact methods may vary between fields. For example, if the signal data are known to be constant, then σ ( displaystyle sigma ) can be calculated using the standard deviation of the signal. If the signal data are not constant, then σ ( displaystyle sigma ) can be calculated from data where the signal is zero or relatively constant. Jump up ^ Often special filters are used to weight the noise : DIN - A, DIN - B, DIN - C, DIN - D, CCIR - 601 ; for video, special filters such as comb filters may be used. Jump up ^ Maximum possible full scale signal can be charged as peak - to - peak or as RMS. Audio uses RMS, Video P-P, which gave + 9 dB more SNR for video. References Jump up ^ Breeding, Andy ( 2004 ). The Music Internet Untangled : Using Online Services to Expand Your Musical Horizons. Giant Path. p. 128. ISBN 9781932340020. Jump up ^ `` Signal - to - noise ratio ''. scholarpedia.org. Jump up ^ Michael A. Choma, Marinko V. Sarunic, Changhuei Yang, Joseph A. Izatt. Sensitivity advantage of swept source and Fourier domain optical coherence tomography. Optics Express, 11 ( 18 ). Sept 2003. Jump up ^ D.J. Schroeder ( 1999 ). Astronomical optics ( 2nd ed. ). Academic Press. p. 433. ISBN 978 - 0 - 12 - 629810 - 9. ^ Jump up to : Bushberg, J.T., et al., The Essential Physics of Medical Imaging, ( 2e ). Philadelphia : Lippincott Williams & Wilkins, 2006, p. 280. Jump up ^ Rafael C. González, Richard Eugene Woods ( 2008 ). Digital image processing. Prentice Hall. p. 354. ISBN 0 - 13 - 168728 - X. Jump up ^ Tania Stathaki ( 2008 ). Image fusion : algorithms and applications. Academic Press. p. 471. ISBN 0 - 12 - 372529 - 1. Jump up ^ Jitendra R. Raol ( 2009 ). Multi-Sensor Data Fusion : Theory and Practice. CRC Press. ISBN 1 - 4398 - 0003 - 0. Jump up ^ John C. Russ ( 2007 ). The image processing handbook. CRC Press. ISBN 0 - 8493 - 7254 - 2. Jump up ^ Rose, Albert ( 1973 ). Vision -- Human and Electronic. Plenum Press. p. 10. ISBN 9780306307324. (... ) to reduce the number of false alarms to below unity, we will need (... ) a signal whose amplitude is 4 -- 5 times larger than the rms noise. Jump up ^ Defining and Testing Dynamic Parameters in High - Speed ADCs -- Maxim Integrated Products Application note 728 Jump up ^ Fixed - Point vs. Floating - Point DSP for Superior Audio -- Rane Corporation technical library External links Taking the Mystery out of the Infamous Formula, `` SNR = 6.02 N + 1.76 dB, '' and Why You Should Care. ( 1 ) Analog Devices ADC and DAC Glossary -- Maxim Integrated Products Understand SINAD, ENOB, SNR, THD, THD + N, and SFDR so you do n't get lost in the noise floor -- Analog Devices The Relationship of dynamic range to data word size in digital audio processing Calculation of signal - to - noise ratio, noise voltage, and noise level Learning by simulations -- a simulation showing the improvement of the SNR by time averaging Dynamic Performance Testing of Digital Audio D / A Converters Fundamental theorem of analog circuits : a minimum level of power must be dissipated to maintain a level of SNR Interactive webdemo of visualization of SNR in a QAM constellation diagram Institute of Telecommunicatons, University of Stuttgart hide Noise ( physics and telecommunications ) General Acoustic quieting Distortion Noise cancellation Noise control Noise measurement Noise power Noise reduction Noise temperature Phase distortion Noise in... Audio Buildings Electronics Environment Government regulation Human health Images Radio Rooms Ships Sound masking Transportation Video Class of noise Additive white Gaussian noise ( AWGN ) Atmospheric noise Background noise Brownian noise Burst noise Cosmic noise Flicker noise Gaussian noise Grey noise Jitter Johnson -- Nyquist noise ( thermal noise ) Pink noise Quantization error ( or q. noise ) Shot noise White noise Coherent noise Value noise Gradient noise Worley noise Engineering terms Channel noise level Circuit noise level Effective input noise temperature Equivalent noise resistance Equivalent pulse code modulation noise Impulse noise ( audio ) Noise figure Noise floor Noise shaping Noise spectral density Noise, vibration, and harshness ( NVH ) Phase noise Pseudorandom noise Statistical noise Ratios Carrier - to - noise ratio ( C / N ) Carrier - to - receiver noise density ( C / kT ) dBrnC E / N ( energy per bit to noise density ) E / N ( energy per symbol to noise density ) Modulation error ratio ( MER ) Signal, noise and distortion ( SINAD ) Signal - to - interference ratio ( S / I ) Signal - to - noise ratio ( S / N, SNR ) Signal - to - noise ratio ( imaging ) Signal to noise plus interference ( SNIR ) Signal - to - quantization - noise ratio ( SQNR ) Contrast - to - noise ratio ( CNR ) Related topics List of noise topics Acoustics Colors of noise Interference ( communication ) Noise generator Radio noise source Spectrum analyzer Thermal radiation Denoise methods General Low - pass filter Median filter Total variation denoising Wavelet denoising 2D ( Image ) Gaussian blur Anisotropic diffusion Bilateral filter Non-local means Block - matching and 3D filtering ( BM3D ) Shrinkage Fields Retrieved from `` https://en.wikipedia.org/w/index.php?title=Signal-to-noise_ratio&oldid=846124197 '' Categories : Engineering ratios Error measures Measurement Electrical parameters Audio amplifier specifications Noise ( electronics ) Statistical ratios Hidden categories : All articles with unsourced statements Articles with unsourced statements from April 2015 Wikipedia articles needing clarification from April 2015 Pages using div col without cols and colwidth parameters Talk Contents About Wikipedia বাংলা Български Català Deutsch Eesti Español فارسی Français Galego 한국어 हिन्दी Italiano עברית Lietuvių Magyar Nederlands 日本 語 Norsk nynorsk Polski Português Română Русский Suomi Svenska Українська Tiếng Việt 中文 19 more Edit links This page was last edited on 16 June 2018, at 13 : 47. 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Question: what is a good signal to noise ratio for audio
Answer: higher than 1:1 (greater than 0 dB)