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, 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.
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.
where A is root mean square (RMS) amplitude (for example, RMS voltage).
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
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 (W) or milliwatts (mW), and the signal-to-noise ratio is a pure number.
However, when the signal and noise are measured in volts (V) or amperes (A), which are measures of amplitude,[note 1] they must first be squared to obtain a quantity proportional to power, as shown below:
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 VRMS).
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'.
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:
But in signal processing and communication, one usually assumes that 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
where 'A' is the amplitude of the AC signal.
where is the signal mean or expected value and is the standard deviation of the noise, or an estimate thereof.[note 2] Notice that such an alternative definition is only useful for variables that are always non-negative (such as photon counts and luminance). 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.
It should be also noted, that this definition is closely related to the Sensitivity Index or d', when assuming that the signal has two states, and the noise does not change between the two states.
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.
Channel signal-to-noise ratio is given by
where W is the bandwidth and is modulation index
Output signal-to-noise ratio (of AM receiver) is given by
Channel signal-to-noise ratio is given by
Output signal-to-noise ratio is given by
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 measurements. 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.
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 Eb/No, 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.
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 2n/1. The formula is then:
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
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 6.02m. The very large dynamic range of floating-point can be a disadvantage, since it requires more forethought in designing algorithms.
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.
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.
[...] 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.
In telecommunications, the carrier-to-noise ratio, often written CNR or C/N, is the signal-to-noise ratio (SNR) of a modulated signal. The term is used to distinguish the CNR of the radio frequency passband signal from the SNR of an analog base band message signal after demodulation, for example an audio frequency analog message signal. If this distinction is not necessary, the term SNR is often used instead of CNR, with the same definition.
Digitally modulated signals (e.g. QAM or PSK) are basically made of two CW carriers (the I and Q components, which are out-of-phase carriers). In fact, the information (bits or symbols) is carried by given combinations of phase and/or amplitude of the I and Q components. It is for this reason that, in the context of digital modulations, digitally modulated signals are usually referred to as carriers. Therefore, the term carrier-to-noise-ratio (CNR), instead of signal-to-noise-ratio (SNR) is preferred to express the signal quality when the signal has been digitally modulated.
High C/N ratios provide good quality of reception, for example low bit error rate (BER) of a digital message signal, or high SNR of an analog message signal.Contrast-to-noise ratio
Contrast-to-noise ratio (CNR) is a measure used to determine image quality. CNR is similar to the metric, signal-to-noise ratio (SNR), but subtracts off a term before taking the ratio. This is important when there is a significant bias in an image, such as from haze. As can be seen in the picture at right, the intensity is rather high even though the features of the image are washed out by the haze. Thus this image may have a high SNR metric, but will have a low CNR metric.
One way to define contrast-to-noise ratio is:
where SA and SB are signal intensities for signal producing structures A and B in the region of interest and σo is the standard deviation of the pure image noise.Eb/N0
Eb/N0 (the energy per bit to noise power spectral density ratio) is an important parameter in digital communication or data transmission. It is a normalized signal-to-noise ratio (SNR) measure, also known as the "SNR per bit". It is especially useful when comparing the bit error rate (BER) performance of different digital modulation schemes without taking bandwidth into account.
As the description implies, Eb is the signal energy associated with each user data bit; it is equal to the signal power divided by the user bit rate (not the channel symbol rate). If signal power is in watts and bit rate is in bits per second, Eb is in units of joules (watt-seconds). N0 is the noise spectral density, the noise power in a 1 Hz bandwidth, measured in watts per hertz or joules.
These are the same units as Eb so the ratio Eb/N0 is dimensionless; it is frequently expressed in decibels. Eb/N0 directly indicates the power efficiency of the system without regard to modulation type, error correction coding or signal bandwidth (including any use of spread spectrum). This also avoids any confusion as to which of several definitions of "bandwidth" to apply to the signal.
But when the signal bandwidth is well defined, Eb/N0 is also equal to the signal-to-noise ratio (SNR) in that bandwidth divided by the "gross" link spectral efficiency in bit/s⋅Hz, where the bits in this context again refer to user data bits, irrespective of error correction information and modulation type.Eb/N0 must be used with care on interference-limited channels since additive white noise (with constant noise density N0) is assumed, and interference is not always noise-like. In spread spectrum systems (e.g., CDMA), the interference is sufficiently noise-like that it can be represented as I0 and added to the thermal noise N0 to produce the overall ratio Eb/(N0 + I0).Emphasis (telecommunications)
Typically, prior to some process, such as transmission over cable, or recording to phonograph record or tape, the input frequency range most susceptible to noise is boosted. This is referred to as "pre-emphasis" – "pre-" the process the signal will undergo. Later, when the signal is received, or retrieved from recording, the reverse transformation is applied ("de-emphasis") so that the output accurately reproduces the original input. Any noise added by transmission or record/playback, to the frequency range previously boosted, is now attenuated in the de-emphasis stage.
The high-frequency signal components are emphasized to produce a more equal modulation index for the transmitted frequency spectrum, and therefore a better signal-to-noise ratio for the entire frequency range.
Emphasis is commonly used in FM broadcasting and vinyl (e.g. LP) records.Fellgett's advantage
Fellgett's advantage or the multiplex advantage is an improvement in signal to noise ratio that is gained when taking multiplexed measurements rather than direct measurements. The name is derived from P. B. Fellgett, who first made the observation as part of his PhD. When measuring a signal whose noise is dominated by detector noise, a multiplexed measurement such as the signal generated by a Fourier transform spectrometer can produce a relative improvement in signal-to-noise ratio (SNR), compared to an equivalent scanning monochromator, of the order of the square root of m, where m is the number of sample points comprising the spectrum.Low-noise amplifier
A low-noise amplifier (LNA) is an electronic amplifier that amplifies a very low-power signal without significantly degrading its signal-to-noise ratio. An amplifier increases the power of both the signal and the noise present at its input. LNAs are designed to minimize additional noise. Designers can minimize additional noise by using low-noise components, operating points, and circuit topologies. Minimizing additional noise must balance with other goals such as power gain and impedance matching.
LNAs are found in radio communications systems, medical instruments and electronic test equipment. A typical LNA may supply a power gain of 100 (20 decibels (dB)) while decreasing the signal-to-noise ratio by less than a factor of two (a 3 dB noise figure (NF)). Although LNAs are primarily concerned with weak signals that are just above the noise floor, they must also consider the presence of larger signals that cause intermodulation distortion.Noise-equivalent power
Noise-equivalent power (NEP) is a measure of the sensitivity of a photodetector or detector system. It is defined as the signal power that gives a signal-to-noise ratio of one in a one hertz output bandwidth. An output bandwidth of one hertz is equivalent to half a second of integration time. The units of NEP are watts per square root hertz. The NEP is equal to the noise spectral density (expressed in units of or ) divided by the responsivity (expressed in units of or , respectively).
A smaller NEP corresponds to a more sensitive detector. For example, a detector with an NEP of can detect a signal power of one picowatt with a signal-to-noise ratio (SNR) of one after one half second of averaging. The SNR improves as the square root of the averaging time, and hence the SNR in this example can be improved by a factor of 10 by averaging 100-times longer, i.e. for 50 seconds.
If the NEP refers to the signal power absorbed in the detector, it is known as the electrical NEP. If instead it refers to the signal power incident on the detector system, it is called the optical NEP. The optical NEP is equal to the electrical NEP divided by the optical coupling efficiency of the detector system.Noise (electronics)
In electronics, noise is an unwanted disturbance in an electrical signal. Noise generated by electronic devices varies greatly as it is produced by several different effects.
In communication systems, noise is an error or undesired random disturbance of a useful information signal. The noise is a summation of unwanted or disturbing energy from natural and sometimes man-made sources. Noise is, however, typically distinguished from interference, for example in the signal-to-noise ratio (SNR), signal-to-interference ratio (SIR) and signal-to-noise plus interference ratio (SNIR) measures. Noise is also typically distinguished from distortion, which is an unwanted systematic alteration of the signal waveform by the communication equipment, for example in signal-to-noise and distortion ratio (SINAD) and total harmonic distortion plus noise (THD+N) measures.
While noise is generally unwanted, it can serve a useful purpose in some applications, such as random number generation or dither.Noise figure
Noise figure (NF) and noise factor (F) are measures of degradation of the signal-to-noise ratio (SNR), caused by components in a signal chain. It is a number by which the performance of an amplifier or a radio receiver can be specified, with lower values indicating better performance.
The noise factor is defined as the ratio of the output noise power of a device to the portion thereof attributable to thermal noise in the input termination at standard noise temperature T0 (usually 290 K). The noise factor is thus the ratio of actual output noise to that which would remain if the device itself did not introduce noise, or the ratio of input SNR to output SNR.
The noise figure is simply the noise factor expressed in decibels (dB).Noise spectral density
In communications, noise spectral density, noise power density, noise power spectral density, or simply noise density (N0) is the power spectral density of noise or the noise power per unit of bandwidth. It has dimension of power over frequency, whose SI unit is watts per hertz (equivalent to watt-seconds).
It is commonly used in link budgets as the denominator of the important figure-of-merit ratios, such as carrier-to-noise-density ratio as well as Eb/N0 and Es/N0.
If the noise is one-sided white noise, i.e., constant with frequency, then the total noise power N integrated over a bandwidth B is N = BN0 (for double-sided white noise, the bandwidth is doubled, so N is BN0/2). This is utilized in signal-to-noise ratio calculations.
For thermal noise, its spectral density is given by N0 = kT, where k is Boltzmann's constant in joules per kelvin, and T is the receiver system noise temperature in kelvins.Peak signal-to-noise ratio
Peak signal-to-noise ratio, often abbreviated PSNR, is an engineering term for the ratio between the maximum possible power of a signal and the power of corrupting noise that affects the fidelity of its representation. Because many signals have a very wide dynamic range, PSNR is usually expressed in terms of the logarithmic decibel scale.Preemphasis improvement
In FM broadcasting, preemphasis improvement is the improvement in the signal-to-noise ratio of the high-frequency portion of the baseband, i.e., modulating signal, which improvement results from passing the modulating signal through a preemphasis network before transmission.
The reason that preemphasis is needed is that the process of detecting a frequency-modulated signal in a receiver produces a noise spectrum that rises in frequency (a so-called triangular spectrum). Without preemphasis, the received audio would sound unacceptably noisy at high frequencies, especially under conditions of low carrier-to-noise ratio, i.e., during fringe reception conditions. Preemphasis increases the magnitude of the higher signal frequencies, thereby improving the signal-to-noise ratio. At the output of the discriminator in the FM receiver, a deemphasis network restores the original signal power distribution.
FM improvement factor is the quotient obtained by dividing the signal-to-noise ratio (SNR) at the output of an FM receiver by the carrier-to-noise ratio (CNR) at the input of the receiver. When the FM improvement factor is greater than unity, the improvement in the SNR is always obtained at the expense of an increased bandwidth in the receiver and the transmission path.
FM improvement threshold is the point in an FM (frequency modulation) receiver at which the peaks in the RF signal equal the peaks of the thermal noise generated in the receiver. A baseband signal-to-noise ratio of about 30 dB is typical at the improvement threshold, and this ratio improves 1 dB for each decibel of increase in the signal above the threshold.Renko chart
A renko chart (Japanese: 練行足, translit. renkōashi, also written 練り足 neriashi) is a type of financial chart of Japanese origin used in technical analysis that measures and plots price changes. A renko chart consists of bricks (煉瓦, renga), which proponents say more clearly show market trends and increase the signal-to-noise ratio compared to typical candlestick charts.Sensitivity (electronics)
The sensitivity of an electronic device, such as a communications system receiver, or detection device, such as a PIN diode, is the minimum magnitude of input signal required to produce a specified output signal having a specified signal-to-noise ratio, or other specified criteria.
Sensitivity is sometimes improperly used as a synonym for responsivity.
The sensitivity of a microphone is usually expressed as the sound field strength in decibels (dB) relative to 1 V/Pa (Pa = N/m2) or as the transfer factor in millivolts per pascal (mV/Pa) into an open circuit or into a 1 kilohm load.
The sensitivity of a loudspeaker is usually expressed as dB / 2.83 VRMS at 1 metre. This is not the same as the electrical efficiency; see Efficiency vs sensitivity.
The sensitivity of a hydrophone is usually expressed as dB re 1 V/µPa.
Sensitivity in a receiver is normally defined as the minimum input signal required to produce a specified signal-to-noise S/N ratio at the output port of the receiver and is defined as the mean noise power at the input port of the receiver times the minimum required signal-to-noise ratio at the output of the receiver:
Because receiver sensitivity indicates how faint an input signal can be to be successfully received by the receiver, the lower power level, the better. Lower power for a given S/N ratio means better sensitivity since the receiver's contribution is smaller. When the power is expressed in dBm the larger the absolute value of the negative number, the better the receive sensitivity. For example, a receiver sensitivity of −98 dBm is better than a receive sensitivity of −95 dBm by 3 dB, or a factor of two. In other words, at a specified data rate, a receiver with a −98 dBm sensitivity can hear signals that are half the power of those heard by a receiver with a −95 dBm receiver sensitivity.Signal-to-interference ratio
The signal-to-interference ratio (SIR or S/I), also known as the carrier-to-interference ratio (CIR or C/I), is the quotient between the average received modulated carrier power S or C and the average received co-channel interference power I, i.e. cross-talk, from other transmitters than the useful signal.
The CIR resembles the carrier-to-noise ratio (CNR or C/N), which is the signal-to-noise ratio (SNR or S/N) of a modulated signal before demodulation. A distinction is that interfering radio transmitters contributing to I may be controlled by radio resource management, while N involves noise power from other sources, typically additive white gaussian noise (AWGN).Signal-to-noise ratio (imaging)
The signal-to-noise ratio (SNR) is used in imaging as a physical measure of the sensitivity of a (digital or film) imaging system. Industry standards measure SNR in decibels (dB) of power and therefore apply the 10 log rule to the "pure" SNR ratio (a ratio of 1:1 yields 0 decibels, for instance). In turn, yielding the "sensitivity." Industry standards measure and define sensitivity in terms of the ISO film speed equivalent; SNR:32.04 dB = excellent image quality and SNR:20 dB = acceptable image quality.Signal to Noise
Signal to Noise may refer to:
Signal-to-noise ratio, a measure used in science and engineering to quantify how much a signal has been corrupted by noise
Signal-to-noise ratio (imaging), this measure specifically in the field of imaging.Spectral signal-to-noise ratio
In applied mathematics, the two-dimensional Spectral signal-to-noise ratio (SSNR) measures the normalised cross-correlation coefficient between several two-dimensional images over corresponding rings in Fourier space as a function of spatial frequency (Unser 1987). It is a multi-particle extension of the Fourier ring correlation (FRC), which is related to the Fourier shell correlation. The SSNR is a popular method for finding the resolution of a class average in cryo-electron microscopy.Wavelet modulation
Wavelet modulation, also known as fractal modulation, is a modulation technique that makes use of wavelet transformations to represent the data being transmitted. One of the objectives of this type of modulation is to send data at multiple rates over a channel that is unknown. If the channel is not clear for one specific bit rate, meaning that the signal will not be received, the signal can be sent at a different bit rate where the signal to noise ratio is higher.
Noise (physics and telecommunications)
|Class of noise|