Analog Comm

Analog Communication C K. C. K Nyakey Analog Communication

Objectives † To introduce the student to the basic principles of modulation and receiver systems † To study the effects of noise in communication systems † .....acquire a good understanding of the fundamental principles of analog communication systems

Analog Communication

Analog Communication † Course Code: TEL 291 † Pre-requisite: None † Credit Hours: 3

Analog Communication

Assessment

¾

Lab: 10%

¾

Test/Quiz/Assignments: 20%

¾

Final Examination: 70%

Analog Communication

Course Outline † Introduction to communication systems † Signals, Linear Systems & Fourier Theory y † Transmission Media † Analog Modulation † Superheterodyne S h t d AM & FM Receivers R i † Monochrome & Colour Television Analog Communication

Literature † Taub & Schilling, "Principles of Comm nication S Communication Systems", stems" McGraw-Hill, McG a Hill 1987 † K. K S. S Shanmugam, Shanmugam "Digital Digital and Analog Communciation Systems", John Wiley & Sons, 1985 † S. Haykin, "Communication Systems", John Wiley & Sons, 3rd Ed., 1994 † P.H. Young, "Electronic Communication Techniques", New Jersey: Prentice-Hall, 3rd Ed 1994 Ed., Analog Communication

Literature † D. Roddy & J. Coolen, "Electronic Comm nications" New Communications", Ne Jersey: Je se PrenticeP entice Hall, 4th Ed., 1995 † B.P. Lathi, "Communications Systems", Wiley, y, 1968 † Schwartz, "Information Transmission, Modulation and Noise", McGraw-Hill, 1990

Analog Communication

What is Analog Communication? † It is the method of transmitting signals where he e data is represented ep esented by b continuously contin o sl variable, measurable, physical quantities, such as length, suc e g , width, d , voltage, o age, or o pressure p essu e † The opposite pp of Analogue g Communication is Digital Communication, which is any communication system that uses digital signals (or digital techniques) in the transmission and reception of messages Analog Communication

What is Analog Communication? † analog is the process of taking an audio or video ideo signal (in most cases cases, the human h man voice) and translating it into electronic pulses pu ses (e.g. (e g voltage o age or o current) cu e ) that a varies a es continuously as the original audio or video signal † Digital on the other hand is breaking the signal into a binary format where the audio or video data is represented by a series of "1"s and "0"s. Analog Communication

What is Analog Communication?

Analog Communication

What is Analog Communication - 2? † Advantages of digital systems „ Di Digital i l offers ff better b sound d & image i quality, li clarity, security and integrity of transmitted data. „ usually require less power to transmit and take up less bandwidth „ …Only Only digitized information can be transported through a noisy channel without degradation Î See Shannon’s theorem!

† Advantages Ad t off digital di it l systems t „ …. Analogue comm. systems are less expensive than digital g comm. systems y Analog Communication

Chapter 1 – Introduction to Communication System

† This chapter chapte serves se es as a review e ie of the fundamentals of telecommunications systems. At the end of this chapter, the student is expected to acquire the following: † † †

Understand the basic physical elements of a telecommunication system. Possess knowledge of the 4 essential requirements for effective information transfer between two points. Understand the importance of signals in communication systems and be able to explain the difference between analogue and digital signals.

Analog Communication

History of Telecoms † †

On 14th February, 1876: Invention of Telephone by Alexander Graham Bell 1881, 5 yrs later – 1st telecom system installed in Ghana (Gold-Coast)

†

1901: Marconi established wireless communication between UK and US.

†

25th March 1925, John Logie Baird invented television

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1948: invention of transistor – 1st Commercial Computer invented in 1951

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Internet – 1973; WWW – 1989 by Tim Berners Lee

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Analogue Cellular Telephones – 1980

†

GSM (2G), 2.5G, 3G – Digital Systems

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What is Communication? † The word communication is used to refer to the sharing or exchanging of information (or messages) between two or more entities.

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Personal Communication

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Data Communication

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Essential Requirements of Communication Sys?

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Elements of a Communication System

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Shannon‘s Shannon s theory † The Shannon theorem states that given a nois channel with noisy ith channel capacit capacity C and information transmitted at a rate R, then if

† there exists a code that allows the probability of error at the receiver to be made arbitrarily small. This means that theoretically, it is possible to transmit information without error at any rate below a limiting rate, rate C. C Analog Communication

Shannon – Hartley theorem

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Exercise 1 † Given that a channel has a bandwidth of 30MH and the Signal-to-Noise 30MHz Signal to Noise ratio atio is 8 8.45 45 dB, find the channel capacity C in Megabits per second. pe seco d

† What is the capacity of a channel with negligible or zero noise?

Analog Communication

Simplex Communication

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Half Duplex Communication

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Full Duplex Communication

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No. Of Sources & Destinations † One – to – One (Point to Point)

† One – to – Many (Broadcast)

† Many – to – Many (Video Conferencing)

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Telecommunication Services † VOICE (Voice telecommunication)

† VIDEO (Video (Vid telecommunication) l i i )

† DATA (Data telecommunication)

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Assignment 1 † Given that a channel has a bandwidth of 70MH and the Signal-to-Noise 70MHz Signal to Noise ratio atio is 8 8.45 45 dB, find the channel capacity C in Gigabits per second pe seco d † A telephone network has a bandwidth of 3 4kHz 3.4kHz. a) Calculate the capacity of the channel for a S/N / ratio of 30dB. b) Calculate the minimum S/N ratio required for information transmission through the channel at the rate of 4800 bits/s. Analog Communication

Chapter 2 Signals, Systems & Fourier theory † Concepts of signals, orthogonal f nction Fo function, Fourier ie theory, theo and correlation for spectral analysis † Linear systems & the impact of noise in the transmission of data † By y the end of this chapter: p Î Goal: Understand signals and data representation in both time & frequency domain Analog Communication

Signals † Signal: Any time varying quantity that can be b used d to t carry information i f ti

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ASCII Encoding of A

† A Î 65 Î 1000001 Î Signal Î TX

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Classification of Signals (1) † Based on 2 factors † How it is represented in time † How its amplitude is allowed to vary

This axis is continuous or discrete

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Classification of Signals (2) † The 4 Basic types of signals are:

† Continuous C ti ti time, cont. t Amplitude A lit d † Continuous time, time discrete amplitude † Discrete time,, continuous amplitude p † Discrete time, discrete amplitude Analog Communication

Classification of Signals (3) † The 4 Basic types of signals are:

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Continuous-time Continuous time Vrs Discrete Discrete-time time

This axis is continuous or discrete

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Continuous-time Continuous time Signal(Sinusoid)

x(t ) = ACos (ωt + ϑ ) T

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= 2π

ω

Discrete-time Signal (1) (Derived from Cont. signal) † Explanatory Notes on Sampling Theory:

† ‘Exact reconstruction of a continuoustime baseband signal from its samples is possible if the signal is bandlimited and the sampling p g frequency q y is g greater than twice the signal bandwidth’.

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Note: AnalogueÎDigital Conversion † Analogue to Digital Conversion requires 3 essential steps: † 1. Sampling: † 2. Quantization † 3. Encoding

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Discrete-time Discrete time Signal (2) † Defined only @ discrete times † E.g., E g Î Exam results per semester † S (n) where n = {…, -1, 0, 1, …}, and are a e functions u c o s de defined ed o on integers. ege s s(n )

s(1 )

s(-1 )

n

s(2 ) -1

0

1

2

3

4

s(5 )

s(3 ) s(4 ) Analog Communication

5

Analog vrs Digital T his axis is continuous or di t t discrtete

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Analog vrs Digital f ( t ) = f (T + t )

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X ( n) = x ( n + N )

Examples of Periodic Signals

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Causal vrs Anti Anti-Causal Causal

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Even vrs Odd Signals

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Even-Odd Even Odd Decomposition(1) † Given a function X (t) of a signal; 1 Ev {x ( t ) } = [x ( t ) + x ( − t ) ] 2

1 Odd {x(t ) } = [x(t ) − x(−t )] 2

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Even-Odd Even Odd Decomposition(1)

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Even-Odd Even Odd Decomposition(1)

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Class Work (5 mins) † Given the function x(t) = 2t + 1 Use the odd-even decomposition concept to show that X(t) = Sum of Ev(x(t)) and Odd(x(t))

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Deterministic vrs Stochastic

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Random Signals (Noise) T

lim 1 n(t ) = T →∞ T

∫ n (t ) dt

−T

T

lim 1 n (t ) = T →∞ T 2

2

2

2

∫ (n(t ))

−T

2

dt

2

The square root of n^2(t) is the rms value of n(t). n(t)

n(t)

0

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t

Random Signals (Noise) † Probability Density Function p(x)

p ( x ) = P{xo ∠x∠xo + δx

}

† Probability that random variable lies b/n x1 and x2: P {x 1 ∠ x ∠ x

x2

2

}= ∫

p ( x ) dx

x1

n(t)

n(t)

0 Analog Communication

t

Systems † Signals are always associated with one or more systems

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Systems Analysis (1) † Characterization of systems is by how many inp ts and o inputs outputs tp ts they the have: ha e „ „ „ „

SISO (Single Input, Input Single Output) SIMO (Single Input, Multiple Outputs) MISO (Multiple Inputs, Single Output) MIMO (Multiple Inputs, Multiple Outputs)

Analog Communication

Systems Analysis (2) † Systems could also be categorized on basis of type t pe of signals signals: „ Analog System (Analog Input/ Analog

Output)

„ Digital System (Digital Input/ Digital Output) „ Systems with Analog Input/ Digital Output or Vice versa

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Systems Analysis (3) Another approach is on whether the system has memory or otherwise! o M Memoryless l systems do d not depend d d on any past input. (In digital electronics – Combinational Logic) o Systems with memory do depend on past input. (In digital electronics – Sequential Logic) o Causal systems do not depend on any future input. Analog Communication

Systems Analysis (4) Finally, systems are categorized by other properties such as: o o o

o o

A system is linear if it has the superposition and scaling p p properties A system that is not linear is non-linear If the output of a system does not depend explicitly on time the system is said to be time time, time-invariant; invariant; otherwise it is time-variant A system that will always produce the same output for a given input is said to be deterministic A system that will produce different outputs for a given input is said to be stochastic

Analog Communication

Linear Systems † Linear systems must satisfy both homogeinity and additivity requirements: † These 2 rules Î referred to as the principle of superposition p p

† Additivity: † Homogeneity: Analog Communication

Linear Systems † Linear systems must satisfy both homogeinit and additivity homogeinity additi it requirements: eq i ements † These 2 rules Î referred to as the principle of superposition † Additivity: † Homogeneity:

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Fourier Transform

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Signal – to – Noise Ratio SNR =

Psignal Pnoise

=

Signal

Power

Noise

Power

⎛ Psignal ⎞ ⎛ Asignal ⎞ ⎟⎟ = 20 log10 ⎜⎜ ⎟⎟ SNR(dB) = 10 log10 ⎜⎜ ⎝ Pnoise ⎠ ⎝ Anoise ⎠

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SNR & Capacity Cal. (Classwork) † Given that the SNR of a channel is 3dB. Ho many How man bits can be transmitted t ansmitted in 11 hour for a given bandwidth of 30kHZ.

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Correlation † Correlation is a measure of how related two entities are a e † A high correlation means that there is a lot of resemblance between the two compared entities.

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Auto Correlation Auto-Correlation † The auto-correlation for a periodic signal of pe iod T is defined as follo period follows: s † It defines how much a function correlates with a time shifted version of itself, with respect to that time shift +

R i (τ ) =

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1 T

T 2

∫ −

T 2

W i ( t ) W i ( t − τ ) dt

Cross Correlation Cross-Correlation † The cross-correlation for periodic signals of pe iod T is defined as: period as † It measures how much two different signals, Wi and Wj, one shifted in time with respect to the other, correlate as a function of that time shift +

1 C ij (τ ) = T Analog Communication

T 2

∫W −

T 2

i

( t )W j ( t − τ ) dt

Orthogonality † Two periodic signals of period T are orthogonal when their crosscross product is null for a zero time shift g signals g can be transmitted at † Two orthogonal the same time and will not interfere with each other. This principle is largely applied in CDMA +

T 2

∫

W

T − 2 Analog Communication

i

( t )W

j

( t ) dt

=

0

Orthogonality †

The vectors (1, 3, 2), (3, −1, 0), (1/3, 1, −5/3) are orthogonal th l to t each h other, th since i (1)(3) + (3)(−1) + (2)(0) = 0, (3)(1/3) + (−1)(1) + (0)(−5/3) = 0, 0 (1)(1/3) + (3)(1) − (2)(5/3) = 0.

†

These vectors are orthogonal, for example (1, 0, 0, 1, 0, 0, 1, 0), (0, 1, 0, 0, 1, 0, 0, 1), (0, 0, 1, 0, 0, 1, 0, 0)

Analog Communication

Power Spectral Density (PSD) † PSD, describes how the power (or variance) of a time series is distributed with frequency † Mathematically, it is defined as the Fourier transform of the auto-correlation sequence of the time series † The term white noise refers to a noise whose power is distributed uniformly over all frequencies. White noise has a flat PSD

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Thermal Noise † …caused by the random motion of molec les at an molecules any temperature tempe at e above abo e absolute zero Kelvin

† Since the 3rd law of thermodynamics prevents one from extracting all heat from a physical system, one cannot reach absolute zero and so cannot entirely avoid thermal noise. Analog Communication

Time & Frequency Domain Rep † Signals can be manipulated (i.e., amplified, filte ed etc.) filtered, etc ) in the time domain † However However, it is often convenient and frequently necessary, when signal analysis and p processing g is required, q , to represent p the signal in the frequency domain

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Time & Frequency Domain Rep

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Time & Frequency Domain Rep

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Mathematical Representation Of Signals in Freq. Domain † The theory of complex numbers is essential in understanding nde standing ffrequency eq enc domain representation. Î Revision Î † In the ff sections, the concepts of Fourier analysis y will provide p us with a powerful p tool for the general transformation of a signal from the time to frequency domain & the inverse transform!

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Euler’s Euler s Identity

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Complex Nos. Examples

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Complex Nos. (Solve)

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Complex Nos. (Solution)

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Fourier Transform (1)

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Joseph Fourier

† Joseph Fourier submitted a paper in 1807 to the Academy of Sciences of Paris. The paper was a mathematical description of problems involving heat conduction, and was at first rejected for lack of mathematical rigour. However, it contained ideas which have developed into an important area of mathematics named in his honour, Fourier analysis. Analog Communication

Fourier Transform (2)

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Classification of signals .. †

Energy and power signals „

A signal is an energy ene g signal if, if and onl only if, if it has nonzero but finite energy for all time:

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Classification of signals .. † A signal is a power signal if, and only if, it has finite but nonzero power for all time:

† General rule: Periodic and random signals are power signals. Signals that are both deterministic and nonperiodic are energy signals Analog Communication

Classification of signals ... † Energy Signal „ B By definition, d fi iti energy signals i l are time ti li limited it d „ That is they exist over a finite interval of time and they are non-periodic „ An energy signal´s total energy is finite and hence the average power is zero „ Eg. are single pulses, a band of pulses and sinusoidal radar pulses

† Power Signal „ They exist over infinite time „ A power signal´s total energy is infinite but the average power is finite „ Eg. Eg are a e sine waves, a es pulse p lse trains, t ains etc. etc Analog Communication

QUESTION † Classify the following signals as energy signals i l or power signals. i l

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Analog Communication