Information about Signal To Noise Ratio
Signal-to-noise ratio (often abbreviated SNR or S/N) is an electrical engineering concept defined as the ratio of a signal power to the noise power corrupting the signal.
In less technical terms, signal-to-noise ratio compares the level of a desired signal (such as music) to the level of background noise. The higher the ratio, the less obtrusive the background noise is.
where P is average power and A is RMS amplitude. Both signal and noise power (or amplitude) must be measured at the same or equivalent points in a system, and within the same system bandwidth.
Because many signals have a very wide dynamic range, SNRs are usually expressed in terms of the logarithmic decibel scale. In decibels, the SNR is, by definition, 10 times the logarithm of the power ratio. If the signal and the noise is measured across the same impedance then the SNR can be obtained by calculating 20 times the base-10 logarithm of the amplitude ratio:
Signal-to-noise ratio is closely related to the concept of dynamic range, where dynamic range measures the ratio between noise and the greatest un-distorted signal on a channel. SNR measures the ratio between noise and an arbitrary signal on the channel, not necessarily the most powerful signal possible. Because of this, measuring signal-to-noise ratios requires the selection of a representative or reference signal. In audio engineering, this reference signal is usually a sine wave, sounding a tone, at a recognized and standardized nominal level 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 general, higher signal to noise is better; the signal is 'cleaner'.
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.
Any measurement device is disturbed by parasitic phenomena. This includes the electronic noise as described above, but also any external event that affects 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 signal's, it is possible to filter it or to process the signal.
When the noise is a random perturbation and the signal is a constant value, it is possible to enhance the SNR by increasing the measurement time.
If we process a Fourier transform on the recorded signal, random noise corresponds to high frequencies: there are variations between two neighbouring points. If the signal is made of broad peaks, then these peaks correspond to low frequencies; the "highest frequency" can be estimated by inverse of the width of the peak.
The modulation error ratio (MER) is a measure of the SNR in a digitally modulated signal. Like SNR, MER can be expressed in dB.
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 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[1] 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.[2]
In online discussion forums such as Usenet, off-topic posts and spam are regarded as "noise" that interferes with the "signal" of appropriate discussion. Another example is Bugzilla, where "please fix this" comments clutter up the discussion without helping to solve the bug.[https://bugzilla.mozilla.org/page.cgi?id=etiquette.html] A system of moderation may improve the SNR by filtering out irrelevant posts.
The wiki collaboration model addresses the same problem in a different way, by permitting users to "moderate" content, ideally adding signal while removing noise.
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In less technical terms, signal-to-noise ratio compares the level of a desired signal (such as music) to the level of background noise. The higher the ratio, the less obtrusive the background noise is.
Technical sense
In engineering, signal-to-noise ratio is a term for the power ratio between a signal (meaningful information) and the background noise:
where P is average power and A is RMS amplitude. Both signal and noise power (or amplitude) must be measured at the same or equivalent points in a system, and within the same system bandwidth.
Because many signals have a very wide dynamic range, SNRs are usually expressed in terms of the logarithmic decibel scale. In decibels, the SNR is, by definition, 10 times the logarithm of the power ratio. If the signal and the noise is measured across the same impedance then the SNR can be obtained by calculating 20 times the base-10 logarithm of the amplitude ratio:
Electrical SNR and acoustics
Often the signals being compared are electromagnetic in nature, though it is also possible to apply the term to sound stimuli. Due to the definition of decibel, the SNR gives the same result independent of the type of signal which is evaluated (such as power, current, or voltage).Signal-to-noise ratio is closely related to the concept of dynamic range, where dynamic range measures the ratio between noise and the greatest un-distorted signal on a channel. SNR measures the ratio between noise and an arbitrary signal on the channel, not necessarily the most powerful signal possible. Because of this, measuring signal-to-noise ratios requires the selection of a representative or reference signal. In audio engineering, this reference signal is usually a sine wave, sounding a tone, at a recognized and standardized nominal level 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 general, higher signal to noise is better; the signal is 'cleaner'.
Image processing and interferometry
In image processing, the SNR of an image is usually defined as the ratio of the mean pixel value to the standard deviation of the pixel values. Related measures are the "contrast ratio" and the "contrast-to-noise ratio".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.
For a measurement device generally speaking
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Recording of the noise of a thermogravimetric analysis device that is poorly isolated in a mechanical point of view; the middle of the curve shows a lower noise, due to a lesser surrounding human activity at night.
Any measurement device is disturbed by parasitic phenomena. This includes the electronic noise as described above, but also any external event that affects 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 signal's, it is possible to filter it or to process the signal.
When the noise is a random perturbation and the signal is a constant value, it is possible to enhance the SNR by increasing the measurement time.
If we process a Fourier transform on the recorded signal, random noise corresponds to high frequencies: there are variations between two neighbouring points. If the signal is made of broad peaks, then these peaks correspond to low frequencies; the "highest frequency" can be estimated by inverse of the width of the peak.
Digital signals
When using digital storage the number of bits of each value determines the maximum signal-to-noise ratio. In this case the noise is the error signal caused by the quantization of the signal, taking place in the analog-to-digital conversion. The noise level is non-linear and signal-dependent; different calculations exist for different signal models. The noise is modeled as an analog error signal being summed with the signal before quantization ("additive noise").The modulation error ratio (MER) is a measure of the SNR in a digitally modulated signal. Like SNR, MER can be expressed in dB.
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 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[1] and uniform distribution. In this case, the SNR is approximately
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:
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.[2]
Notes
- Analog-to-digital converters have other sources of noise that decrease the SNR compared to the theoretical maximum from the idealized quantization noise.
- Often special filters are used to weight the noise: DIN-A, DIN-B, DIN-C, DIN-D, CCIR-601, and special filters in video - comb filter.
- 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.
- It is more common to express SNR in digital systems using Eb/No - the energy per bit per noise power spectral density.
- Further information: Quantization noise, Bit resolution
Informal use
Informally, "signal-to-noise ratio" refers to the ratio of useful information to false or irrelevant data.In online discussion forums such as Usenet, off-topic posts and spam are regarded as "noise" that interferes with the "signal" of appropriate discussion. Another example is Bugzilla, where "please fix this" comments clutter up the discussion without helping to solve the bug.[https://bugzilla.mozilla.org/page.cgi?id=etiquette.html] A system of moderation may improve the SNR by filtering out irrelevant posts.
The wiki collaboration model addresses the same problem in a different way, by permitting users to "moderate" content, ideally adding signal while removing noise.
See also
- Audio system measurements
- Video quality
- Subjective video quality
- Near-far problem
- Peak signal-to-noise ratio
- SINAD (ratio of signal-including-noise-and-distortion to noise-and-distortion only)
- ENOB
- Eb/N0
- Es/N0
- Carrier to Noise Ratio (CNR or C/N)
- Carrier-to-receiver noise density (C/N0)
- Carrier-to-Interference Ratio (CIR or C/I)
- Carrier-to-Noise-and-Interference Ratio (CIR or C/I)
- Contrast to Noise Ratio
- SQNR (Signal-to-Quantization Noise Ratio)
- Total harmonic distortion
- Noise figure
References
1. ^ Defining and Testing Dynamic Parameters in High-Speed ADCs — Maxim Integrated Products Application note 728
2. ^ Fixed-Point vs. Floating-Point DSP for Superior Audio — Rane Corporation technical library
2. ^ Fixed-Point vs. Floating-Point DSP for Superior Audio — Rane Corporation technical library
External links
- ADC and DAC Glossary - Maxim Integrated Products
- Understand SINAD, ENOB, SNR, THD, THD + N, and SFDR so you don'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
Electrical engineering (sometimes referred to as electrical and electronic engineering) is an engineering field that deals with the study and/or application of electricity, electronics and electromagnetism.
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In physics, power (symbol: P) is the rate at which work is performed or energy is transmitted, or the amount of energy required or expended for a given unit of time.
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signal is any time-varying quantity. Signals are often scalar-valued functions of time (waveforms), but may be vector valued and may be functions of any other relevant independent variable.
The concept is broad, and hard to define precisely.
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The concept is broad, and hard to define precisely.
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In science, and especially in physics and telecommunication, noise is fluctuations in and the addition of external factors to the stream of target information (signal) being received at a detector.
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In mathematics, root mean square (abbreviated RMS or rms), also known as the quadratic mean, is a statistical measure of the magnitude of a varying quantity. It is especially useful when variates are positive and negative, e.g. waves.
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Bandwidth is the difference between the upper and lower cutoff frequencies of, for example, a filter, a communication channel, or a signal spectrum, and is typically measured in hertz.
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logarithm (to base b) of a number x is the exponent y that satisfies x = by. It is written logb(x) or, if the base is implicit, as log(x).
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The decibel (dB) is a logarithmic unit of measurement that expresses the magnitude of a physical quantity (usually power) relative to a specified or implied reference level.
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decimal (base ten or occasionally denary) numeral system has ten as its base. It is the most widely used numeral system, perhaps because humans have four fingers and a thumb on each hand, giving a total of ten digits over both hands.
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logarithm (to base b) of a number x is the exponent y that satisfies x = by. It is written logb(x) or, if the base is implicit, as log(x).
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amplitude is a nonnegative scalar measure of a wave's magnitude of oscillation, that is, the magnitude of the maximum disturbance in the medium during one wave cycle.
Sometimes this distance is called the peak amplitude
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Sometimes this distance is called the peak amplitude
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Electromagnetism is the physics of the electromagnetic field: a field which exerts a force on particles that possess the property of electric charge, and is in turn affected by the presence and motion of those particles.
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Sound is a disturbance of mechanical energy that propagates through matter as a wave (through fluids as a compression wave, and through solids as both compression and shear waves).
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The decibel (dB) is a logarithmic unit of measurement that expresses the magnitude of a physical quantity (usually power) relative to a specified or implied reference level.
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Dynamic range is a term used frequently in numerous fields to describe the ratio between the smallest and largest possible values of a changeable quantity, such as in sound and light.
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A distortion is the alteration of the original shape (or other characteristic) of an object, image, sound, waveform or other form of information or representation. Distortion is usually unwanted.
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Channel, in communications (sometimes called communications channel), refers to the used to convey information from a sender (or transmitter) to a receiver.
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Sound is a disturbance of mechanical energy that propagates through matter as a wave (through fluids as a compression wave, and through solids as both compression and shear waves).
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Engineering is the applied science of acquiring and applying knowledge to design, analysis, and/or construction of works for practical purposes. The American Engineers' Council for Professional Development, also known as ECPD,[1] (later ABET [2]
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sine wave or sinusoid is a function that occurs often in mathematics, physics, signal processing, electrical engineering, and many other fields. Its most basic form is:
which describes a wavelike function of time (t) with
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which describes a wavelike function of time (t) with
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Pitch is the perceived fundamental frequency of a sound. While the actual fundamental frequency can be precisely determined through physical measurement, it may differ from the perceived pitch because of overtones, or partials, in the sound.
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Nominal level is the operating level at which an electronic signal processing device is designed to operate. The electronic circuits that make up such equipment are limited in the maximum signal they can output and the low-level internally-generated electronic noise they add to the
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The alignment level in an audio signal chain or on an audio recording is a defined anchor point that represents a reasonable or typical level. It does not represent a particular sound level or signal level or digital representation, but it can be defined as corresponding to
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DBU can refer to:
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- Dansk Boldspil-Union, in English known as the Danish Football Association
- dBu, a decibel measurement of voltage
- 1,8-Diazabicyclo(5.4.
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IMAGE (from Imager for Magnetopause-to-Aurora Global Exploration), or Explorer 78, was a NASA MIDEX mission that studied the global response of the Earth's magnetosphere to changes in the solar wind.
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- the arithmetic mean (and is distinguished from the geometric mean or harmonic mean).
- the expected value of a random variable, which is also called the population mean.
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In probability and statistics, the standard deviation of a probability distribution, random variable, or population or multiset of values is a measure of the spread of its values. It is usually denoted with the letter σ (lower case sigma).
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The contrast ratio is a measure of a display system, defined as the ratio of the luminosity of the brightest color (white) to that of the darkest color (black) that the system is capable of producing.
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For other uses, see Power (physics).
Optical power (dioptric power or refractive power) is the degree to which a lens or mirror converges or diverges light. It is equal to the reciprocal of the focal length of the device...... Click the link for more information.
Voltage (sometimes also called electric potential difference or electrical tension) is the potential similarity of electrical potential between two points of an electrical or electronic circuit, expressed in volts.
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