Gaussian Noise

By: Anchal Arora13MCA0157

Gaussian noise is statistical noise having

a probability distribution function (PDF) equal to that of the normal distribution, which is also known as the Gaussian distribution.

The probability density function  of a Gaussian random variable  is given by:

where  represents ‘ž ‘the grey level,  ’ μ ‘the  mean value and ’ σ’ the standard deviation.

In telecommunications, computer

networking, communication channels and digital images.

Now they can be affected by  Gaussian noise coming from many natural sources, such as the thermal vibrations of atoms in conductors  from the earth and other warm objects, and from celestial sources such as the Sun.

Where can it happen ?

Noise in Digital images

Noise in imaging systems is usually either

additive or multiplicative. It deals only with additive noise which is zero-mean and white. White noise is spatially uncorrelated: the noise for each pixel is independent and identically distributed .

Gaussian noise provides a good model of noise in many imaging systems

Noise in Images

Principal sources of Gaussian noise in digital

images arise during acquisition e.g. sensor noise caused by poor illumination and/or high temperature, and/or transmission e.g. electronic circuit noise. 

In digital image processing Gaussian noise can be reduced using a spatial filter, though when smoothing an image, an undesirable outcome may result in the blurring of fine-scaled image edges and details because they also correspond to blocked high frequencies.

In image processing, a Gaussian blur (also

known as Gaussian smoothing) is the result of blurring an image by a Gaussian function. It is a widely used effect in graphics software, typically to reduce image noise and reduce detail.

Gaussian blur

Sometimes Gaussian noise is deliberately

added in the images to secure it from the hackers.

Example: Cryptography with images.

Used for security

The performance of wireless communication

systems is highly determined by noise. Particularly if signals are in a fade, the signal-to-noise ratio can be low and bursts of error can occur.

 The wireless systems, in particular cellular systems with dense frequency reuse, are interface limited rather than noise limited.

Noise in wireless Communication

However, any (digital) signal processing

algorithm that attempts to remove, cancel or attenuate such interference increases the noise.

The ability to separate multiple interfering signals is critically determined by the signal-to-noise ratio.

A basic and generally accepted model for thermal noise in communication channels, is the set of assumptions that The noise is additive, i.e., the received signal

equals the transmit signal plus some noise, where the noise is statistically independent of the signal.

The noise is white, i.e, the power spectral density is flat, so the auto correlation of the noise in time domain is zero for any non-zero time offset.

The noise samples have a Gaussian distribution.

Additive White Gaussian Noise (AWGN)

The Gaussian function is used in numerous

research areas: – It defines a probability distribution for noise or data. – It is a smoothing operator. – It is used in mathematics.

The Gaussian function has important properties which are verified with The Gaussian function has important properties which are verified with respect to its integral:

Gaussian Filters

In probabilistic terms, it describes 100% of the

possible values of any given space when varying from negative to positive values given space when varying from negative to positive values.

Gauss function is never equal to zero. It is a symmetric function.

The Gaussian filter is a non-uniform low pass

filter. Central pixels have a higher weighting than

those on the periphery. Gaussian filters might not preserve image

brightness.

Common Characterstics

BIT ERROR RATE

WHAT is Bit Error

Rate? The bit error rate (BER) is the number

of bit errors per unit time. Thebit error ratio (also BER) is the number of bit errors divided by the total number of transferred bits during a studied time interval.

 BER is a unitless performance measure, often expressed as a percentage.

The bit error probability pe is

the expectation value of the bit error ratio. The bit error ratio can be considered as an approximate estimate of the bit error probability. This estimate is accurate for a long time interval and a high number of bit errors.

PACKET ERROR RATIO

The packet error ratio (PER) is the number of incorrectly received data packets divided by the total number of received packets. A packet is declared incorrect if at least one bit is erroneous. The expectation value of the PER is denoted packet error probability pp, which for a data packet length of N bits can be expressed as:

BIT ERROR RATE IN TRANSMISSION

In telecommunication transmission, the bit error rate (BER) is the percentage of bits that have errors relative to the total number of bits received in a transmission, usually expressed as ten to a negative power.

For example, a transmission might have a BER of 10 to the minus 6, meaning that, out of 1,000,000 bits transmitted, one bit was in error. 

The BER is an indication of how often

a packetor other data unit has to be retransmitted.

 Too high a BER may indicate that a slower data rate would actually improve overall transmission time for a given amount of transmitted data since the BER might be reduced, lowering the number of packets that had to be resent because of an error.

BERT (TESTER)

A BERT (bit error rate test or tester) is a procedure or device that measures the BER for a given transmission.

A bit error rate tester (BERT), also known as a bit error ratio tester.

The main building blocks of a BERT are: Pattern generator, which transmits a defined test

pattern to the test system Error detector connected to the test system, to count

the errors generated by or test system Clock signal generator to synchronize the pattern

generator and the error detector Digital communication analyser is optional to display

the transmitted or received signal. Electrical-optical converter and optical-electrical

converter for testing optical communication signals.

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