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EC2252 – COMMUNICATION THEORY IV Sem ECE – R.Vanitha Asst.Prof./ECE

MAHALAKSHMI ENGINEERING COLLEGE

QUESTION BANK

DEPARTMENT: ECE SEMESTER: IV

SUBJECT CODE / Name: EC2252 – COMMUNICATION THEORY

UNIT-III NOISE THEORY

PART-A

1. What is the classification of random process? give one example for each

(AUC MAY 2006)

Stationary and Nonstationary random process

A random process whose statistical characteristics do not change with time

Random process X(t) and X(t+ε) have the same statistical properties In other words, time

translation of a sample function results in another sample function of the random process having

the same probability Example of stationary random process: noise If the statistical

characteristics depend on time, it is called nonstationary random processExample of

nonstationary random process: temperature

2. Define random process? (AUC NOV 2006)

An RV that is a function of time (or any other variable) is called a random process or stochastic

process. The collection of all possible waveform is known as ensemble of the random process

x(t).A waveform in the collection is called a sample function. Sample function amplitudes at

some instant are the values taken by the RV in various trials

3. Define noise figure (AUC MAY 2008)


It is simply defined as the ratio between input signal to noise ratio and output signal to noise

ratio. Noise figure of amplifier is defined as the ratio of the total noise density in

the load to the noise power density delivered to the load due to the source

4. What is white noise? (AUC MAY 2011) (AUC DEC 2010) (AUC MAY 2008)

Many types of noise sources are Gaussian and have flat spectral density over a wide

frequency range. Such spectrum has all frequency components in equal portion, and is

therefore called white noise. The power spectral density of white noise is independent of

the operating frequency.

And it is also defined as noise in idealized form is known as white noise. This means that

in a communication system, the noise analysis is based on an idealized form of noise, is

white noise.

5. Define noise equivalent bandwidth (AUC MAY 2008)

6. What is partition noise? (AUC MAY 2008)

It is generated whenever a current has to divide between two or more electrodes and

result from random fluctuation in the division. It would be expected therefore that a diode

would be less noisy than a transistor, if the third electrode draws current. For this

reason, the input stage of microwave receiver is often a diode circuit which has been


developed for low noise microwave amplification. The spectrum of the partition noise is

flat

7. Draw the auto correlation function and power spectral density of white noise.

(AUC MAY 2008)

8. Define noise factor (AUC NOV 2008)

S/ N at the input

Noise Factor F = _________________

S/ N at the output

S/N = Signal power / Noise Power

9. Define noise temperature (AUC MAY 2004)(AUC NOV 2008)


10. Calculate noise figure and equivalent noise temperature for a receiver connected to an

antenna whose resistance is 100Ω and equivalent noise resistance is 50Ω?

(AUC NOV 2008)

11. State central limit theorem. (AUC NOV 2008)

12. Give the characteristic of shot noise (AUC MAY 2009)

o Shot noise consists of random fluctuations of the electric current in electrical

conductors, which are caused by the fact that the current is carried by discrete

charges (electrons).

o The strength of this noise increases for growing magnitude of the average

current flowing through the conductor.

o Shot noise is to be distinguished from current fluctuations in equilibrium, which

happen without any applied voltage and without any average current flowing.

o These equilibrium current fluctuations are known as Johnson-Nyquist noise.


o Shot noise is important in electronics, telecommunication, and fundamental

physics.

o The strength of the current fluctuations can be expressed by giving the variance

of the current I, where <I> is the average ("macroscopic") current.

o However, the value measured in this way depends on the frequency range of

fluctuations

13. Define shot noise and thermal noise?(AUC MAY 2010)(AUC MAY 2009)

Shot noises arise in active devices due to random behaviour of charge carriers. In

electron tubes, shot noise is generated due to random emission of electrons from

cathodes, whereas in semiconductor devices shot noise is generated due to random

diffusion of minority carriers or simply random generation and recombination of electron-

hole pairs.

The thermal noise or white noise or Johnson noise is the random noise which is

generated in a resistor or the resistive component of complex impedance due to rapid

and random motion of the molecules, atoms and electrons.

14. A receiver connected to an antenna resistance of 50Ω has an equivalent noise

resistance of 30Ω. Find the receiver noise figure.(AUC MAY 2010)

Ra=50Ω,Req=30Ω

Noise Figure=1+req/Ra =1+30/15= 16

15. Define a random variable. Specify the sample space and the random variable for a

coin tossing experiment.(AUC DEC 2010)

Eg:Sample space-Head, Tail

Random variable : 1 for w=Head

0 for w=Tail

16. Write the Rayleigh and Rician probability density functions(AUC MAY 2011)


Let R is the random variable and r to represent the value assumed by the random

variable

The Rayleigh probability density function is defined by

: fR(r) = (r/σ2) e^ (-r2/2 σ2)

The raician distribution is useful for nalysis of carrier sinusoidal signal passing through

narrowband noisy channel.The Rician Distribution expressed as

17. When i s a random process called deterministic?(AUC DEC 2011) (AUC MAY 2010)

A process is called deterministic, if the futures value of any sample function can be

predicted from past values.

Eg: considered the random process x(t)=Acos (wt).In this the knowledge of the sample

function prior to any time instant automatically allows prediction of the future values of

the sample function since its form is known.

18. Two resistors of 20 KΩ, 50 KΩ are at room temperature (290 K). For a bandwidth

of 100 KHz, calculate the thermal noise voltage generated by the two resistors in series

E02=4KTΔfReq

=4*1.38*10-23*290*100*103*70*103

=10.58µV

19. Define random variable. Specify the sample space and the random variable for a coin

tossing experiment(AUC MAY 2012)

The functional relationship which is assigas a real number x(λ) to each possible

outcomes λ of a random experiment is called random variable.

Sample space =Head,Tail

20. Give the definition of the noise equivalent temperature(AUC MAY 2012)

It is the amount of incident signal temperature that would needed to match the internal

noise of the detector such that signal to noise ration is equal to one.


PART-B

1. Explain the following terms(i)Random variable (ii)Gaussian process(iii) Shot noise

(iv) Noise temperature (AUC NOV 2006)ii) Write a short note on shot noise and also

explain about power spectral density of shot noise. (8)(AUC MAY 2010) Discuss the type’s

causes and effects of various forms of noise created within a receiver? (AUC NOV

2008)

- In probability theory and statistics, a Gaussian process is a stochastic process whose

realizations consist of random values associated with every point in a range of times (or of space) such that each such random variable has a normal distribution.

- Moreover, every finite collection of those random variables has a multivariate normal distribution.

Gaussian processes are important in statistical modeling because of properties inherited from the normal distribution.

- For example, if a random process is modeled as a Gaussian process, the distributions of various derived quantities can be obtained explicitly.

- Such quantities include: the average value of the process over a range of times; the error in estimating the average using sample values at a small set of times.

A process is Gaussian if and only if for every finite set of indices t1, ..., tk in the index

set Tis a vector-valued Gaussian random variable. Using characteristic functions of

random variables, the Gaussian property can be formulated as follows: Xt ; t ∈ T is

Gaussian if and only if, for every finite set of indices t1, ..., tk, there are reals σl j with σi

i > 0 and reals μj


2. Explain the following terms (i)Thermal noise(ii)White noise(ii)Narrow band noise

(iv) Random noise (AUC NOV 2006) (ii) Write short notes on shot noise (6) (AUC MAY

2012) (ii)What causes thermal noise in a material? Write the expression for RMS values

of the noise.(AUC MAY 2012) What is thermal noise in communication? What are the

different types of noise? Explain. (ii) Write short notes on shot noise. (6)(AUC DEC

2010) (AUC MAY 2009)

THERMAL NOISE:


WHITE NOISE

Narrow band noise


3. Explain in detail about the white noise and filtered noise (AUC NOV 2008)


Flicker noise is the one appearing in transistors operating at low audio frequencies. Flicker noise is produced at low frequencies (below few KHz).This noise is also called as flicker noise (1/f noise).

4. Explain the following terms 1Statistical average, correlation, covariance and ergodicity?

ERGODICITY


5. Discuss the properties of Gaussian process? (AUC MAY 2008) State and prove four

properties of Gaussian process(AUC MAY 2011)

ergodicity


6. i) Determine the overall noise figure of a three stage cascade amplifier; each stage

having a power gain of 10dB and noise figure of 6dB?

7. i)Give a random process, X (t) = A cos(ωt+ θ), where Aandω a re constants and θ is a

uniform random variable. Show that X (t) is ergodic in both mean and autocorrelation. (8

8. (i) A mixer stage has a noise figure of 20 dB and this i s preceded by an amplifier that

has a noise figure of 9 dB and an available power gain of 15 dB. Calculate the overall

noise figure referred to the input. (8)

Noise figure of an amplifier F1=9dB

Noise figure of mixer F2=20dB

Available power gain of an amplifer A1=15db

F1= in ratio =Antilog10(9/10)=7.94

F2= in ratio =Antilog10(20/10)=100


A1= in ratio =Antilog10(15/10)=31.62

F=F1+f2-1/A1

F=7.99+100-1/31.62

=11.07

F= in dB= 10 log 10(Fratio)= 10 log 10(11.07)=1044dB

(ii) A receiver has a noise figure of 12 dB and it is fed by a low noise amplifier that has a

gain of 50 dB and a noise temperature of 90 K. Calculate the noise temperature of the

receiver and the overall noise temperature of the receiving system. Take room

temperature as 290 K. (8)(AUC DEC 2010)

Receiver noise figure F2=12dB

Amplifier gain G1=50dB

Amplifer noise figure Te1=900l

F2 in db = 10 log F1=12 =15.84

Similarly G1 in db = 50 db =100000

Noise temperature related to noise factor

Te2=(F2-1)T0

T0=290 0K

9. Consider two amplifiers are connected in cascade. First stage amplifier has gain and

noise figure as 10 dB and 2 dB. Second stage has noise figure of 3 dB.

(AUC MAY 2011)

Noise figure of first stage amplifier F1=2dB

Noise figure of second stage amplifier F2=3dB

Noise figure of first stage amplifier Ga=10dB

F=F1-F2-1/Ga =2+3-1/10 =2.2

10. State any 5 properties of autocorrelation function(10)


11. When is a random process said to be strict stationary (SSS), wide sense stationary(WSS)

and ergodicprocess (6)(AUC DEC 2011) (i)List the different type of random process and

give the definitions(10)


12. Explain Narrowband Noise. Show that a narrow band noise n(t) can be represented in

terms of its in phase and qudrature phase components. Write t he details about narrow

band noise and t he properties of quadrature components of narrowband noise.

(16)(AUC MAY 2010) ii) Discuss the properties of narrow band noise. (AUC MAY 2008)


13. Thermal noise from a measured as 4*10-17 W at a temperature of 200 C for a given

bandwidth. What will be the Noise power when temperature is changed to 500

(AUC DEC 2011)

Average noise power Pn=kTB

4*10-17=k(200)B---1

X= k(500)B---2

Divide eqn 1&2

X=10-16W

14. Write the definition, power spectral density and autocorrelation function for white noise and

narrow band noise(filtered white noise)(10)


15. (i)Derive the representation of narrow band noise in terms of envelop and phase

component and list out its properties (i)Derive the representation of narrow band noise in

terms of envelop and phase component and list out its properties


16. Explain in detail about Noise Equivalent Bandwidth

mahalakshmi · o shot noise consists of random fluctuations of the electric ... calculate the...

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