# Is noise a random process?

I have some confusion in noise signals and their nature. Can any one explain how the nature of noise signals is. Is noise a random process.

• Random additions to your signal are noise, but not all noise is random. – Olin Lathrop Nov 8 '12 at 21:00

Adding to @Kaz's answer, noise is normally modeled as a random process. Even an interfering RF carrier or hum can be modeled as a random process (random phase sinusoid).

The theory of random processes is very elegant and allows for simple analysis of systems with "noise".

Moreover, even deterministic components such as quantization or rounding errors are modeled as random processes (independent of the actual signal) in order to study system performance. And these approximations are quite good in general.

• this answer cleared all my doubts.. – nbsrujan Nov 9 '12 at 8:46

What I've been trying to promote is a more nuanced classification system. While it all can be classified as "noise" - i.e. an unwanted signal most noise specialists view things the following way:

1. Interference: Signals from other parts of the circuitry or from outside sources that are unwanted. Best characterized by the possibility of removal through additive or subtractive methods. Emphasis on possible. Ultimately fixable in design or through modification. EMI/RFI effects are one example.
2. Artifacts: non-linear or mixing effects in the circuit that in some cases are like case 1 , possibly removable or in some other cases behave like case 3. Third order effects in ADC's and conversion tones and spectral splatter in ADC's are examples.
3. Noise: Fundamental independent noise processes that are stationary and are characterized by probability distribution functions. Typically poisson or gaussian noise processes that follow RSS (Root sum of squares) addition (i.e. addition of energies). Fundamentally not removable but possibly can be reduced. Johnston, shot noise and telegraph noise.

Treating "noise" (the general term) this way allows someone to understand the possibility of abatement and analysis since mathematically they are treated very differently.

Noise is any difference between the pure signal that is desired by the engineer, and the actual signal. Well, not any difference, but a difference not related to that signal.

For example, an unwanted attenuation of some band of frequencies isn't noise, and neither is distortion.

Noise does not have to be random. An unwanted periodic signal, like power line hum or radio frequency interference, are not random, but are noise.

What is regarded as a proper signal in one circuit becomes noise if it crosses in an unwanted way into another circuit.

Your question is probably about noise generated within devices, such as Johnson noise. Such noise is random.

• When we do theoretical analysis of noise we evaluate power spectral density and analyze many related properties. So when we do analysis do we take noise as random process and do analysis. – nbsrujan Nov 8 '12 at 20:20
• No, distortion most definitely is a form of noise, for must understandings of "noise". – Olin Lathrop Nov 8 '12 at 20:59

Actually the noise is a random process which can follow different probability distributions.White noise is supposed to be having the Gaussian distribution for calculations.when you read about fading in signals which can be due to signal overlapping or distortion due to reflection the noise or the disturbance is modeled by distributions like Rayleigh or Nakagami.