White-Noise-new

What is white noise?

In communication systems, the noise is an error or undesired random disturbance of a useful information signal, introduced before or after the detector and decoder. The noise is a summation of unwanted or disturbing energy from natural and sometimes man-made sources.

Noise is, however, typically distinguished from interference, (e.g. cross-talk, deliberate jamming or other unwanted electromagnetic interference from specific transmitters), for example in the signal-to-noise ratio (SNR), signal-to-interference ratio (SIR) and signal-to-noise plus interference ratio (SNIR) measures. Noise is also typically distinguished from distortion, which is an unwanted alteration of the signal waveform, for example in the signal-to-noise and distortion ratio (SINAD). In a carrier-modulated passband analog communication system, a certain carrier-to-noise ratio (CNR) at the radio receiver input would result in a certain signal-to-noise ratio in the detected message signal. In a digital communications system, a certain Eb/N0 (normalized signal-to-noise ratio) would result in a certain bit error rate (BER).

In figure 1 shows a communication system where the channel experiences attenuation, time delay (precisely known) and additive noise. Most disturbances, interference, attenuation, etc. are usually classified as noise. The most important type of noise that occur in communication system is said to be “white noise”, n(t) that will be discuss later.

Thermal noise

Johnson–Nyquist noise (sometimes thermal, Johnson or Nyquist noise) is unavoidable, and generated by the random thermal motion of charge carriers (usually electrons), inside an electrical conductor, which happens regardless of any applied voltage.

Thermal noise is approximately white, meaning that its power spectral density is nearly equal throughout the frequency spectrum. The amplitude of the signal has very nearly a Gaussian probability density function. A communication system affected by thermal noise is often modeled as an additive white Gaussian noise (AWGN) channel.

The root mean square (RMS) voltage due to thermal noise, generated in a resistance R (ohms) over bandwidth Δf (hertz), is given by

                                                                  

Where 

k_B is Boltzmann's constant (joules per kelvin)

T is the resistor's absolute temperature (kelvin).

In figure 2 shows a thermal noise detection procedure by taking across the terminal of resistance through a sensitive ac voltmeter or by a oscilloscope.

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