White Noise - Free MCQ Practice Test with solutions, GATE ECE Engineering

The spectral density of white noise is Uniform and the autocorrelation function of White noise is the Delta function.

The power spectral density is basically the Fourier transform of the autocorrelation function of the power signal, i.e.

Also, the inverse Fourier transform of a constant function is a unit impulse.

The power spectral density of white noise is given by:

S_X(f) = η / 2 for all frequency 'f', i.e.

Now auto-correlation is inverse Fourier transform (IFT) of power spectral density function.

The inverse Fourier transform of the power spectrum of white noise will be an impulse as shown:

Concept:

For binary modulation scheme:

Probability of Error (P_e) =

Where d_min = distance between two signaling

N₀ = Noise power spectral density

Calculation:

From fig d₁ = (-1, 1)

d₂ = (1, 2)

distance between ‘2’ point d_min =

By default,

Noise power spectral density is considered two-sided.

P_e = Q[1000]

Statement a:

Noise in communication systems is generally divided into two categories-

i) External noise like atmospheric noise, industrial noise solar noise, and cosmic noise.

ii) Internal noise like shot noise, thermal noise, low and high-frequency noise. (Statement a is false)

Statement b:

Noise temperature is one way of expressing the level of available noise power introduced by a component or source. The power spectral density of the noise is expressed in terms of the temperature (in kelvins) that would produce that level of Johnson–Nyquist noise.

It is useful in dealing with UHF. (Statement b is True)

Statement c:

Internal and external noises are the main source of noise in the receiver (Statetemt c is false)

Note:

Thermal Agitation:

• It is also called Johnson-Nyquist noise
• It is distributed across the entire frequency spectrum range so it is also called as white noise
• Thermal noise is generally observed in the passive component like R, L & C due to the random movement of charge carriers electrons.
• Random noise power is

Pn = KTB

Where,

K = Boltz man's constant

T = temperature

B = Bandwidth over which noise is measured

High- Frequency Noise:

• These noises are also known as TRANSIT- TIME Noise
• They are observed in the semiconductor devices when the transit time of a charge carrier while crossing a junction is compared with the time period of that signal

White noise is that signal whose frequency spectrum is uniform i.e. it has flat spectral density.

The power spectral density (PSD) of white noise is uniform throughout the frequency spectrum as shown:

Shot noise:

• It is a type of noise that appears in all amplifying & active devices.
• It is associated with a current flow
• The noise caused by random variations in the arrival of electrons or holes at the output electrode of an amplifying device is called shot noise.
• In semiconductor devices, shot Noise is due to the random variation in the diffusion of minority carriers
• Current is a flow of carriers each of which carriers a finite amount of charge.
• For diodes, the exact expression for RMS shot noise 
  

​Shot noise:

• shot noise produced by ‘particle-like behavior of electrons and photons when an external excitation is available to produce current.
• Shot noise is avoidable only if we reduce all current to zero.
• Shot noise in optical devices is widely called ‘quantum noise’.

Hence the option (C) is correct

White noise is that signal whose frequency spectrum is uniform i.e. it has flat spectral density.

The power spectral density (PSD) of white noise is uniform throughout the frequency spectrum as shown:

The AWGN has constant power spectral density.

White noise is a idealized process with two sided spectral density equal to constant N0/2 and frequencies varying from minus infinity to plus infinity. Thus the average noise power is infinity.