The document discusses Gaussian noise, which refers to statistical noise that follows a normal distribution. It is commonly found in digital images, telecommunications systems, and other contexts. Some key points made in the document include: - Gaussian noise arises from natural sources like thermal vibrations and has a probability density function given by the normal distribution. - In digital images, it provides a good model for sensor and transmission noise and can be reduced using spatial filters, though this may also blur details. - It is commonly used to model thermal noise in communication channels, where it is assumed to be additive, white, and have a Gaussian distribution. - Bit error rate and packet error ratio are measures of noise that indicate the need

1. By: Anchal Arora
13MCA0157

2. 
 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.

3. 
 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 ?

4. 
Noise in Digital images

5. 
 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

6. 
 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.

7. 
 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

8. 

9. 
 Sometimes Gaussian noise is deliberately added in
the images to secure it from the hackers.
 Example: Cryptography with images.
Used for security

10. 
 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

11. 
 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.

12. 
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)

13. 

14. 
 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

15. 
 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.

16. 
 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

18. 
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.

19. 
 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.

20. 

21. 
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:

22. 
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.

23. 
 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.

24. 
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.

25. 
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.

26. 
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