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In this post I want to discuss Noise Spectral Density.

# Noise Spectral Density

Noise Spectral Density or Noise Density, (N_{o}) is a measurement of the noise power per Hertz. For white noise, which is constant with respect to frequency we can simply divide the total noise power by the bandwidth of the system. Assuming that thermal noise is the predominant form of noise in our system, recall the formula for thermal noise:

P = kTB

This means that the Noise Density is simply:

N_{o} = kT

where:

k = Boltzmann Constant (1.38064852 x 10^{-23})

T = Temperature in degrees Kelvin.

At a normal operating temperature of 290° Kelvin, the typical Noise Density is just under 4.004×10^{-21} Watts/Hz, or on the decibel scale -173.975 dBm/Hz. This produces a total noise power of -100.96 dBm in a 20MHz wide channel.

## Other Types of Noise

What if you are calculating the noise density for a type of noise that is NOT constant with frequency, for instance grey noise? In this case, The Noise Power and Noise Density would both be functions of frequency. The Noise Density would be the derivative of the Noise Power with respect to frequency. The total Noise Power is the integral of the Noise Density with respect to frequency.

Thankfully, most noise types in communications systems can be approximated as white noise, and we can leave out the calculus for now!

## Useful Information

Here is a great video from the guys at Analog Devices that explains how to convert Noise Spectral Density to RMS Noise and the assumptions we should be aware of!