In communications, noise spectral density (NSD), noise power density, noise power spectral density, or simply noise density (''N''
0) is the
power spectral density
The power spectrum S_(f) of a time series x(t) describes the distribution of power into frequency components composing that signal. According to Fourier analysis, any physical signal can be decomposed into a number of discrete frequencies, ...
of
noise
Noise is unwanted sound considered unpleasant, loud or disruptive to hearing. From a physics standpoint, there is no distinction between noise and desired sound, as both are vibrations through a medium, such as air or water. The difference arise ...
or the
noise power In telecommunication, the term noise power has the following meanings:
# The measured total noise in a given bandwidth at the input or output of a device when the signal is not present; the integral of noise spectral density over the bandwidth
# T ...
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 Space (mathematics), mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any Point (geometry), point within it. Thus, a Line (geometry), lin ...
of
power
Power most often refers to:
* Power (physics), meaning "rate of doing work"
** Engine power, the power put out by an engine
** Electric power
* Power (social and political), the ability to influence people or events
** Abusive power
Power may a ...
over
frequency
Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is eq ...
, whose
SI unit
The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric system and the world's most widely used system of measurement. E ...
is watt per hertz (equivalent to
watt-second
The joule ( , ; symbol: J) is the unit of energy in the International System of Units (SI). It is equal to the amount of work done when a force of 1 newton displaces a mass through a distance of 1 metre in the direction of the force applied ...
or
joule
The joule ( , ; symbol: J) is the unit of energy in the International System of Units (SI). It is equal to the amount of work done when a force of 1 newton displaces a mass through a distance of 1 metre in the direction of the force applied ...
).
It is commonly used in
link budget
A link budget is an accounting of all of the power gains and losses that a communication signal experiences in a telecommunication system; from a transmitter, through a communication medium such as radio waves, cable, waveguide, or optical fibe ...
s as the denominator of the important figure-of-merit ratios, such as
carrier-to-noise-density ratio
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 b ...
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.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 the 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 kinetic energy of particles in a gas with the thermodynamic temperature of the gas. It occurs in the definitions of the kelvin and the gas constant, ...
in joules per kelvin, and ''T'' is the receiver
system
A system is a group of Interaction, interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded and influenced by its environment (systems), environment, is described by its boundaries, ...
noise temperature
In electronics, noise temperature is one way of expressing the level of available noise power introduced by a component or source. (This is to be distinguished from Temperature Noise in Thermodynamics or Principal Interferrometric Analysis Over C ...
in
kelvin
The kelvin, symbol K, is the primary unit of temperature in the International System of Units (SI), used alongside its prefixed forms and the degree Celsius. It is named after the Belfast-born and University of Glasgow-based engineer and phys ...
s.
The noise amplitude spectral density is the square root of the noise power spectral density, and is given in units such as
.
See also
*
Noise-equivalent bandwidth
The Fourier transform of a function of time, s(t), is a complex-valued function of frequency, S(f), often referred to as a frequency spectrum. Any linear time-invariant operation on s(t) produces a new spectrum of the form H(f)•S(f), which chan ...
*
Spectral density estimation
*
Welch's method
Welch's method, named after Peter D. Welch, is an approach for spectral density estimation.
It is used in physics, engineering, and applied mathematics for estimating the power of a signal at different frequencies.
The method is based on the ...
References
*
{{DEFAULTSORT:Noise Spectral Density
Noise (electronics)
Frequency-domain analysis
Acoustics