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In communications, noise spectral density (NSD), noise power density, noise power spectral density, or simply noise density (N₀) is the power spectral density of noise or the noise power per unit of bandwidth. It has dimension of power over frequency, whose SI unit is watt per hertz (equivalent to watt-second or joule). 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/N₀ and E_s/N₀.

If the noise is one-sided white noise, i.e., constant with frequency, then the total noise power N integrated over a bandwidth B is N = BN₀ (for double-sided white noise, the bandwidth is doubled, so N is BN₀/2). This is utilized in signal-to-noise ratio calculations.

For thermal noise, its spectral density is given by N₀ = kT, where k is the Boltzmann constant in joules per kelvin, and T is the receiver system noise temperature in kelvins.

The noise amplitude spectral density is the square root of the noise power spectral density, and is given in units such as $\mathrm {V} /{\sqrt {\mathrm {Hz} }}$ .^[1]^[2]

References

^ Michael Cerna & Audrey F. Harvey (2000). "The Fundamentals of FFT-Based Signal Analysis and Measurement" (PDF). Amplitude spectral density is computed as … The units are then in Vrms/√Hz or V/√Hz
^ "FFT Spectrum and Spectral Densities – Same Data, Different Scaling". Audio Precision. Retrieved 2021-02-16. The Amplitude Spectral Density is also used to analyze noise signals. It has units of V/√ Hz in the analog domain and FS/√ Hz in the digital domain.

Jerry C. Whitaker (27 April 2005). The Electronics Handbook, Second Edition. CRC Press. p. 636. ISBN 978-1-4200-3666-4.

[1] Michael Cerna & Audrey F. Harvey (2000). "The Fundamentals of FFT-Based Signal Analysis and Measurement" (PDF). Amplitude spectral density is computed as … The units are then in Vrms/√Hz or V/√Hz

[2] "FFT Spectrum and Spectral Densities – Same Data, Different Scaling". Audio Precision. Retrieved 2021-02-16. The Amplitude Spectral Density is also used to analyze noise signals. It has units of V/√ Hz in the analog domain and FS/√ Hz in the digital domain.

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+{{Short description|Noise power per unit of bandwidth}}
-{{Unreferenced|date=October 2006}}
-In communications, '''noise spectral density''' '''''N''<sub>0</sub>''' is the [[Electronic noise|noise]] power per unit of bandwidth; that is, it is the [[power spectral density]] of the noise. It has dimension of '''power'''/'''frequency''' (see [[dimensional analysis]]), whose SI coherent unit is watts per hertz, which is equivalent to watt-seconds. If the noise is [[white noise]], i.e., constant with frequency, then the total noise power ''N'' in a bandwidth ''B'' is ''BN''<sub>0</sub>. This is utilized in [[signal-to-noise ratio]] calculations.
+In communications, '''noise spectral density''' ('''NSD'''), '''noise power density''', '''noise power spectral density''', or simply '''noise density''' (''N''<sub>0</sub>) is the [[power spectral density]] of [[Electronic noise|noise]] or the [[noise power]] per unit of [[Bandwidth (signal processing)|bandwidth]]. It has [[dimensional analysis|dimension]] of [[power (physics)|power]] over [[frequency]], whose [[SI unit]] is watt per hertz (equivalent to [[watt-second]] or [[Joule (unit)|joule]]).
+It is commonly used in [[link budget]]s as the denominator of the important figure-of-merit ratios, such as [[carrier-to-noise-density ratio]] as well as [[Eb/N0|''E''<sub>''b''</sub>/''N''<sub>0</sub>]] and [[Es/N0|''E''<sub>''s''</sub>/''N''<sub>0</sub>]].
+If the noise is one-sided [[white noise]], i.e., constant with frequency, then the total noise power ''N'' integrated over a bandwidth ''B'' is ''N''&nbsp;=&nbsp;''BN''<sub>0</sub> (for double-sided white noise, the bandwidth is doubled, so ''N'' is ''BN''<sub>0</sub>/2). This is utilized in [[signal-to-noise ratio]] calculations.
-The [[thermal noise]] density is given by ''N''<sub>0</sub>&nbsp;= ''kT'', where '''k''' is [[Boltzmann's constant]] in joules per [[kelvin]], and '''''T''''' is the receiver [[system]] [[noise temperature]] in kelvins.
+For [[thermal noise]], its spectral density is given by ''N''<sub>0</sub>&nbsp;=&nbsp;''kT'', where ''k'' is the [[Boltzmann constant]] in joules per kelvin, and ''T'' is the receiver [[system]] [[noise temperature]] in [[kelvin]]s.
-'''''N<sub>0</sub>''''' is commonly used in [[link budget]]s as the denominator of the important figure-of-merit ratios [[Eb/N0|''E''<sub>''b''</sub>/''N''<sub>0</sub>]] and [[Es/N0|''E''<sub>''s''</sub>/''N''<sub>0</sub>]].
+The '''noise amplitude spectral density''' is the square root of the noise power spectral density, and is given in units such as <math>\mathrm{V}/\sqrt{\mathrm{Hz}}</math>.<ref>{{cite web|author1=Michael Cerna|author2=Audrey F. Harvey|year=2000|title=The Fundamentals of FFT-Based Signal Analysis and Measurement|url=http://www.lumerink.com/courses/ece697/docs/Papers/The%20Fundamentals%20of%20FFT-Based%20Signal%20Analysis%20and%20Measurements.pdf|quote=Amplitude spectral density is computed as … The units are then in Vrms/√Hz or V/√Hz|name-list-style=amp}}</ref><ref>{{Cite web|title=FFT Spectrum and Spectral Densities – Same Data, Different Scaling|url=https://www.ap.com/blog/fft-spectrum-and-spectral-densities-same-data-different-scaling/|access-date=2021-02-16|website=Audio Precision|language=en-US|quote=The Amplitude Spectral Density is also used to analyze noise signals. It has units of V/√ Hz  in the analog domain and FS/√ Hz in the digital domain.}}</ref>
+== See also ==
+*[[Noise-equivalent bandwidth]]
+*[[Spectral density estimation]]
+*[[Welch's method]]
+== References ==
+<references/>
+*{{cite book|author=Jerry C. Whitaker|title=The Electronics Handbook, Second Edition|url=https://books.google.com/books?id=FdSQSAC3_EwC&pg=PA636|date=27 April 2005|publisher=CRC Press|isbn=978-1-4200-3666-4|pages=636}}
 {{Noise}}
 {{DEFAULTSORT:Noise Spectral Density}}
-[[Category:Noise]]
+[[Category:Noise (electronics)]]
+[[Category:Frequency-domain analysis]]
+[[Category:Acoustics]]