Noise spectral density

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 ${\displaystyle \mathrm {V} /{\sqrt {\mathrm {Hz} }}}$.^[1][2]

See also

• Noise-equivalent bandwidth
• Spectral density estimation
• Welch's method

References

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.

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