In communications, noise spectral density (NSD), noise power density, noise power spectral density, or simply noise density (''N''
0) is the
power spectral density
In signal processing, the power spectrum S_(f) of a continuous time signal x(t) describes the distribution of power into frequency components f composing that signal. According to Fourier analysis, any physical signal can be decomposed into ...
of
noise
Noise is sound, chiefly unwanted, unintentional, or harmful sound considered unpleasant, loud, or disruptive to mental or hearing faculties. From a physics standpoint, there is no distinction between noise and desired sound, as both are vibrat ...
or the
noise power per unit of
bandwidth
Bandwidth commonly refers to:
* Bandwidth (signal processing) or ''analog bandwidth'', ''frequency bandwidth'', or ''radio bandwidth'', a measure of the width of a frequency range
* Bandwidth (computing), the rate of data transfer, bit rate or thr ...
. It has
dimension
In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus, a line has a dimension of one (1D) because only one coo ...
of
power over
frequency
Frequency is the number of occurrences of a repeating event per unit of time. Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio ...
, whose
SI unit
The International System of Units, internationally known by the abbreviation SI (from French ), is the modern form of the metric system and the world's most widely used system of units of measurement, system of measurement. It is the only system ...
is watt per hertz (W/Hz), equivalent to
watt-second
The joule ( , or ; symbol: J) is the unit of energy in the International System of Units (SI). In terms of SI base units, one joule corresponds to one kilogram-metre, metre squared per second, second squared One joule is equal to the amount ...
(Ws) or
joule
The joule ( , or ; symbol: J) is the unit of energy in the International System of Units (SI). In terms of SI base units, one joule corresponds to one kilogram- metre squared per second squared One joule is equal to the amount of work d ...
(J).
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
''E''''b''/''N''0 and
''E''''s''/''N''0.
If the noise is one-sided
white noise
In signal processing, white noise is a random signal having equal intensity at different frequencies, giving it a constant power spectral density. The term is used with this or similar meanings in many scientific and technical disciplines, i ...
, i.e., constant with frequency, then the total noise power ''N'' integrated over a bandwidth ''B'' is ''N'' = ''BN''
0 (for double-sided white noise, the bandwidth is doubled, so ''N'' is ''BN''
0/2). This is utilized in
signal-to-noise ratio
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 noise power, often expressed in deci ...
calculations.
For
thermal noise
A thermal column (or thermal) is a rising mass of buoyant air, a convective current in the atmosphere, that transfers heat energy vertically. Thermals are created by the uneven heating of Earth's surface from solar radiation, and are an example ...
, its spectral density is given by ''N''
0 = ''kT'', where ''k'' is the
Boltzmann constant
The Boltzmann constant ( or ) is the proportionality factor that relates the average relative thermal energy of particles in a ideal gas, gas with the thermodynamic temperature of the gas. It occurs in the definitions of the kelvin (K) and the ...
in joules per kelvin (J/K), and ''T'' is the receiver
system
A system is a group of interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded and influenced by its open system (systems theory), environment, is described by its boundaries, str ...
noise temperature
In electronics, noise temperature is one way of expressing the level of available noise power introduced by a component or source. The power spectral density of the noise is expressed in terms of the temperature (in kelvins) that would produce ...
in
kelvin
The kelvin (symbol: K) is the base unit for temperature in the International System of Units (SI). The Kelvin scale is an absolute temperature scale that starts at the lowest possible temperature (absolute zero), taken to be 0 K. By de ...
s.
The noise amplitude spectral density is the square root of the noise power spectral density, and is given in units such as volts per square root of hertz,
.
See also
*
Noise-equivalent bandwidth
*
Spectral density estimation
*
Welch's method
References
*
{{DEFAULTSORT:Noise Spectral Density
Noise (electronics)
Frequency-domain analysis
Acoustics