User:GyroMagician/Physics

Electronic noise is a random fluctuation in an electrical signal, a characteristic of all electronic circuits. Noise generated by electronic devices varies greatly, as it can be produced by several different effects. Thermal noise and shot noise are inherent to all devices, while other types depend mostly on manufacturing quality and semiconductor defects.

The noise level in an electronic system is typically measured as an electrical power N in watts or dBm, a root mean square (RMS) voltage (identical to the noise standard deviation) in volts, dBμV or a mean squared error (MSE) in volts squared. Noise may also be characterized by its probability distribution and noise spectral density N0(f) in watts per hertz.

A noise signal is typically considered as a linear addition to a useful information signal. Typical signal quality measures involving noise are signal-to-noise ratio (SNR or S/N), signal-to-quantization noise ratio (SQNR) in analog-to-digital coversion and compression, peak signal-to-noise ratio (PSNR) in image and video coding, Eb/N0 in digital transmission, carrier to noise ratio (CNR) before the detector in carrier-modulated systems, and noise figure in cascaded amplifiers.

While noise is generally unwanted, it can serve a useful purpose in some applications, such as random number generation or dithering.

Noise floor
This phenomenon limits the minimum signal level that any radio receiver can usefully respond to, because there will always be a small but significant amount of thermal noise arising in its input circuits. This minimum signal, together with the background noise of the universe, remaining since Big bang, can be referred to as the noise floor. This is why radio telescopes, which search for very low levels of signal from stars, use front-end circuits, usually mounted on the aerial dish, cooled to a very low temperature in liquid nitrogen.

Quantification
Noise is a random process, characterized by stochastic properties such as its variance, distribution, and spectral density. The spectral distribution of noise can vary with frequency, so its power density is measured in watts per hertz (W/Hz). As the power in a resistive element is proportional to the square of the voltage across it, noise voltage (density) can be described by taking the square root of the noise power density, resulting in volts per root hertz ($$\scriptstyle V/\sqrt{Hz}$$). Integrated circuit devices, such as operational amplifiers commonly quote equivalent input noise level in these terms (at room temperature).

Noise levels are usually viewed relative to signal levels, often quoted as a signal-to-noise ratio (SNR). Telecommunication systems strive to increase the ratio of signal level to noise level in order to effectively transmit data. In practice, if the transmitted signal falls below the level of the noise (often designated as the noise floor) in the system, data can no longer be decoded at the receiver. Noise levels in telecommunication systems are a product of both internal and external sources to the system.

Noise in telecommunications
In communication systems, noise is an error or undesired disturbance of a useful information signal, before or after the detector and decoder. The noise is a summation of unwanted or disturbing energy introduced from several sources, both man-made and natural. However, noise is often distinguished from interference such as cross-talk or deliberate jamming, using a measure such as signal-to-noise plus interference (SNIR). Noise is also typically distinguished from distortion, i.e. unwanted alteration of the waveform. See for example signal-to-noise and distortion ratio (SINAD). In a carrier-modulated passband analog communication system, a certain carrier-to-noise ratio (CNR) in the radio receiver input would result in a certain signal-to-noise ratio in the detected message signal. In a digital communications system, a certain Eb/N0 would result in a certain bit error rate (BER).

In telecommunication engineering, noise level is usually measured in Watts or decibels (dB) relative to a standard power, usually indicated by adding a suffix after dB. Examples of electrical noise-level measurement units are dBu, dBm0, dBrn, dBrnC, and dBrn(f1 − f2), dBrn(144-line).

Noise (telecommunications) (copy of original page pre-merge)
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. In communications, it may be deliberate as for instance jamming of a radio or TV signal, but in most cases it is assumed to be merely undesired interference with intended operations. Natural and deliberate noise sources can provide both or either of random interference or patterned interference. Only the latter can be cancelled effectively in analog systems; however, digital systems are usually constructed in such a way that their quantized signals can be reconstructed perfectly, as long as the noise level remains below a defined maximum, which varies from application to application.

More specifically, in physics, the term noise has the following meanings:
 * 1) An undesired disturbance within the frequency band of interest; the summation of unwanted or disturbing energy introduced into a communications system from man-made and natural sources.
 * 2) A disturbance that affects a signal and that may distort the information carried by the signal.
 * 3) Random variations of one or more characteristics of any entity such as voltage, current, or data.
 * 4) A random signal of known statistical properties of amplitude, distribution, and spectral density.
 * 5) Loosely, any disturbance tending to interfere with the normal operation of a device or system.

Noise and what can be done about it has long been studied. Claude Shannon established information theory and in so doing clarified the essential nature of noise and the limits it places on the operation of electronic equipment.

ENOB
Dynamic range


 * $$ \mathrm{DR_{ADC}} = 20 \times \log_{10} \left(\frac{2^\Delta}{1}\right) = \left ( 6.02 \cdot \Delta \right )\ \mathrm{dB}$$

SQNR
As the input signal is unknown, it is useful to use statistical methods to characterise the error due to quantisation. Assume a sinusoidal input signal $$x(t)$$. The quantised signal


 * $$x_n(t) = x(t) + \epsilon$$

where $$\epsilon$$ is the error due to quantisation, and $$p_\epsilon$$

Assume a sinusoidal input signal of the form $$x(t) = A \cos \left( \omega_0 t + \phi \right)$$, where the signal amplitude $$A = \frac{M\Delta}{2}$$, $$\Delta$$ is the quantisation step size, $$M = 2^b$$ is the number of quantisation levels, and $$b$$ is the number of bits in the digitised signal.

The variance of the input signal $$x$$ is:


 * $$\sigma_x^2 = \frac{A^2}{2} = \frac{\left(M \Delta /2 \right)^2}{2} = \frac{2^{2b} \Delta^2}{8}$$

WE NEED TO FIGURE OUT WHY

Error signal can be approximated as a sawtooth
 * $$\epsilon = st, \qquad -\frac{\Delta}{2s} < t < \frac{\Delta}{2s}$$

The mean-square error is then
 * $$\bar{\epsilon^2} = \frac{s}{\Delta} \int_{-\Delta/2s}^{\Delta/2s} \epsilon^2\,dt = \frac{\Delta^2}{12}$$


 * $$\sigma_q^2 = \frac{\Delta^2}{12}$$


 * $$SQNR = \frac{\sigma_x^2}{\sigma_q^2} = \frac{2^{2b} \Delta^2}{8} \cdot \frac{12}{\Delta^2} = \frac{3}{2} \cdot 2^{2b}$$

Converting to decibels, we find
 * $$SQNR_{dB} = 10 \log_{10}(3/2) + 2b \cdot 10 \log_{10}(2)$$

which is commonly presented as
 * $$SQNR_{dB} = 6.02 \cdot b + 1.76$$ (for sinusoid)


 * $$SQNR_{dB} = 6.02 \cdot b$$ (for uniform PDF)