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## Signal-to-noise ratio

"Signal-to-noise" redirects here. For statistics, see Effect size. For other uses, see Signal-to-noise (disambiguation).

Signal-to-noise ratio (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.

SNR, bandwidth, and 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 Alternate definition

3 Modulation system measurements

3.1 Amplitude modulation

3.2 Frequency modulation

4 Noise reduction 5 Digital signals 5.1 Fixed point 5.2 Floating point 6 Optical signals

7 Types and abbreviations

## Definition

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Signal-to-noise ratio is defined as the ratio of the power of a signal (meaningful input) to the power of background noise (meaningless or unwanted input):

{\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.

Depending on whether the signal is a constant (s) or a random variable (S), the signal-to-noise ratio for random noise N becomes:[1]

{\displaystyle \mathrm {SNR} ={\frac {s^{2}}{\mathrm {E} [N^{2}]}}}

where E refers to the expected value, i.e. in this case the mean square of N, or

{\displaystyle \mathrm {SNR} ={\frac {\mathrm {E} [S^{2}]}{\mathrm {E} [N^{2}]}}}

If the noise has expected value of zero, as is common, the denominator is its variance, the square of its standard deviation N.

The signal and the noise must be measured the same way, for example as voltages across the same impedance. The root mean squares can alternatively be used in the ratio:

{\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

{\displaystyle P_{\mathrm {signal,dB} }=10\log _{10}\left(P_{\mathrm {signal} }\right)}

and

{\displaystyle P_{\mathrm {noise,dB} }=10\log _{10}\left(P_{\mathrm {noise} }\right).}

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

{\displaystyle \mathrm {SNR_{dB}} =10\log _{10}\left(\mathrm {SNR} \right).}

Using the definition of SNR

{\displaystyle \mathrm {SNR_{dB}} =10\log _{10}\left({\frac {P_{\mathrm {signal} }}{P_{\mathrm {noise} }}}\right).}

Using the quotient rule for logarithms

{\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:

{\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 (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:

{\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)=2\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 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).

स्रोत : en.wikipedia.org

## What is Signal to Noise Ratio and How to calculate it?

Proper signal to noise ratio calculations is design critical and functionally required.

## What is Signal to Noise Ratio and How to calculate it?

Published Date MARCH 17, 2022 Author

As a teenager, while learning the ins and outs of car audio, I often basked in the sheer detail of every note. For me, music was intoxicating, almost as much as the fields of Science and Electronics. However, during this time, the onset of the compact disc and, of course, the car subwoofer was taking center stage.

Before the compact disc, vinyl was the clear-cut choice for audio reproduction, in terms of listening pleasure. However, many would argue that it still is, under certain conditions. Moreover, the CD was a game-changer back then, and the clarity it afforded versus the cassette tape was undeniable. Just like there was a demand for devices to play the new 4K video standard of today, the same was true for the compact disc.

Which, of course, ushered in the car audio CD receiver. With its superior clarity and ease of use, the CD receiver’s reign was complete. However, where there is capitalism, you are sure to find direct competition. This was most certainly the case for the CD receiver, and the most taunted difference the high-end car audio components could use to sway their customers was superior clarity. The clarity that they were speaking of was only achievable through their superior signal to noise ratio specifications.

The one specification that was always better than the lesser brands was their signal to noise ratio (SNR). Furthermore, even to the untrained ear, the difference in the clarity and musical presence was undeniable. So, if SNR can make that much of a difference in musical sound clarity, then its importance in signal transmission applications is exponentially more critical. Therefore, over the next few paragraphs, I will discuss SNR and how to calculate it to ensure design accuracy.

What is Signal to Noise Ratio?

In terms of definition, SNR or signal-to-noise ratio is the ratio between the desired information or the power of a signal and the undesired signal or the power of the background noise.

Also, SNR is a measurement parameter in use in the fields of science and engineering that compares the level of the desired signal to the level of background noise. In other words, SNR is the ratio of signal power to the noise power, and its unit of expression is typically decibels (dB). Also, a ratio greater than 0 dB or higher than 1:1, signifies more signal than noise.

Aside from the technical definition of SNR, the way I define it in other terms is by using a comparative. For example, say that you and one other person are inside a large room having a conversation. However, the room is full of other people who are also having conversations. Furthermore, a few of the other individuals also have similar voice patterns to you and the other individual involved in your discussion. As you can imagine, it would be difficult to decipher which person is saying what.

Why is Signal to Noise Ratio Important?

In the previous comparison, you can get a better understanding of what is meant by an unwanted signal or noise. As you can also imagine, it would be nearly impossible to understand the other party involved in your conversation. Also, in a scenario such as this, we would consider this to be a signal to noise issue or the equivalent of a signal to noise ratio that is below acceptable parameters.

Now suppose the desired signal is essential data with a strict or narrow tolerance for errors, and there are other signals disrupting your desired signal. Again, it would make the task of the receiver exponentially more challenging to decipher the desired signal. In summary, this is what makes having a high signal to noise ratio so important. Furthermore, in some cases, this can also mean the difference in a device functioning or not, and in all cases, it affects performance between transmitter and receiver.

In wireless technology, the key to device performance is the device’s ability to distinguish the applied signals as legitimate information from any background noise or signals on the spectrum. This epitomizes the definition of the standards SNR specifications are utilized to set. Furthermore, the standards I am referring to ensure proper wireless functionality, as well.

## The Basics of Signal to Noise Ratio Calculations

In basic terms, SNR is the difference between the desired signal and the noise floor. Also, in terms of definition, the noise floor is the specious background transmissions that are produced by other devices or by devices that are unintentionally generating interference on a similar frequency. Therefore, to ascertain the signal to noise ratio, one must find the quantifiable difference between the desired signal strength and the unwanted noise by subtracting the noise value from the signal strength value.

Achieving your desired signal integrity can be difficult at any stage of designing.

## What is signal

Signal-to-noise ratio measures the strength of a desired signal relative to background noise. Learn to calculate it and the disturbances that can cause noise.

DEFINITION

## signal-to-noise ratio (S/N or SNR)

Robert Sheldon

John Burke, Nemertes Research

### What is the signal-to-noise ratio?

In analog and digital communications, a signal-to-noise ratio, often written S/N or SNR, is a measure of the strength of the desired signal relative to background noise (undesired signal). S/N can be determined by using a fixed formula that compares the two levels and returns the ratio, which shows whether the noise level is impacting the desired signal.

The ratio is typically expressed as a single numeric value in decibels (dB). The ratio can be zero, a positive number or a negative number. A signal-to-noise ratio over 0 dB indicates that the signal level is greater than the noise level. The higher the ratio, the better the signal quality.

For example, a Wi-Fi signal with S/N of 40 dB will deliver better network services than a signal with S/N of 20 dB. If a Wi-Fi signal's S/N is too low, network performance can be impacted because it becomes more difficult for devices to distinguish the desired signal from the noise. This can result in dropped packets and data retransmissions, leading to lower throughput and higher latency.

Noise includes any unwanted disturbance that degrades the quality of the desired signal. It can include thermal, quantum, electronic, impulse or intermodulation noise, as well as other forms of noise. Environmental factors, such as temperature and humidity, can also affect noise levels.

If the noise is significant enough in comparison to the desired signal -- that is, S/N is low -- it can disrupt a wide range of data transfers, including text files, graphics, telemetry, applications, and audio and video streams.

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A low signal-to-noise ratio can result in dropped packets and data retransmission on a network.

Communications engineers always strive to maximize S/N. Traditionally, this has been done by using the narrowest possible receiving-system bandwidth consistent with the data speed desired. However, there are other methods. For example, engineers might use spread spectrum techniques to improve system performance, or they might boost the signal output power to increase S/N.

In some high-level systems, such as radio telescopes, internal noise is minimized by lowering the temperature of the receiving circuitry to near-absolute zero (-273 degrees Celsius or -459 degrees Fahrenheit). In wireless systems, it is always important to optimize the performance of the transmitting and receiving antennas.

### How do you calculate the signal-to-noise ratio?

The signal-to-noise ratio is typically measured in decibels and can be calculated by using a base 10 logarithm. The exact formula depends on how the signal and noise levels are measured, though.

For example, if they're measured in microvolts, the following formula can be used:

S/N = 20 log10(Ps/Pn)

Ps is the signal in microvolts, and Pn is the noise in microvolts.

However, if the signal and noise are measured in watts, the formula is slightly different:

S/N = 10 log10(Ps/Pn)

The letter P is often used in these formulas to indicate power.

When Ps equals Pn, S/N will be 0. A ratio of 0 dB indicates that the signal is competing directly with the noise level, resulting in a signal that borders on unreadable. In digital communications, this can cause a reduction in data speed because of frequent errors that require the transmitting system to resend data packets.

When Ps is greater than Pn, S/N will be positive. Ideally, Ps should be much greater than Pn to minimize noise interference. As an example, suppose that Ps equals 10 microvolts and Pn equals 1 microvolt. Because 10 divided by 1 equals 10, the following formula can be used to calculate S/N:

S/N = 20 log10(10) = 20 dB

A ratio of 20 dB means that the signal is clearly readable. If the signal is much weaker but still above the noise level -- say, 1.3 microvolts -- S/N is much lower, in this case, only 2.28 dB:

S/N = 20 log10(1.3) = 2.28 dB

This is a marginal situation that could impact network performance, although it's not the worst possible situation. When Ps is less than Pn, S/N is negative, a low signal-to-noise ratio. In this type of situation, reliable communication is nearly impossible, and steps should be taken to increase the signal level, decrease the noise level or implement a combination of both.

This was last updated in August 2021

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