Principles Of Modern Communications - Digital Communications

Principles of Modern CommunicationsDigital Communicationsbased on 2011 lecture series by Dr. S. Waharte.Department of Computer Science and Technology,University of Bedfordshire.14th January 2013

OutlineModernCommunicationsDavid GoodwinUniversity ofBedfordshireDigitalCommunicationsAmplitude Modulation1 Digital Communications2 Amplitude Modulation90

ModernCommunicationsDavid GoodwinUniversity cationsAmplitude Modulation90

Transmission FundamentalsLearning ObjectivesModernCommunicationsDavid GoodwinUniversity ofBedfordshireDigitalCommunications4Amplitude Modulation901Familiarize with signals and systems2Understand the Fourier transform and frequencyrepresentation3Understand the structure and terminology of a digitalcommunication system

Transmission FundamentalsSignals and SystemsModernCommunicationsDavid GoodwinUniversity ofBedfordshireDigitalCommunications5Amplitude Modulation90

Transmission FundamentalsSignal CategoriesModernCommunications Continuous/Analog signal - Varies continuously with time Discrete/Digital signal - Maintains a constant level over someDavid GoodwinUniversity ofBedfordshireDigitalCommunications6Amplitude Modulation90time duration and then switches into another level Periodic signal - Its pattern its repeated after a specific timeduration (signal period). Non-periodic signal – The opposite of periodic, i.e., itspattern is not repeated.

Sine Wave Review - 1ModernCommunicationsDavid GoodwinUniversity ofBedfordshireDigitalCommunications We all know that the Sine of an angle is the opposite side7Amplitude Modulation90divided by the hypotenuse, i.e.

Sine Wave Review - 2ModernCommunicationsDavid GoodwinUniversity ofBedfordshireDigitalCommunications8Amplitude Modulation90

Sine Wave Review - 3ModernCommunicationsDavid GoodwinUniversity ofBedfordshireDigitalCommunications9Amplitude Modulation90

Sine Wave Review - 4ModernCommunicationsDavid GoodwinUniversity ofBedfordshireDigitalCommunications10Amplitude Modulation90

Sine Wave Review - 5ModernCommunicationsDavid GoodwinUniversity ofBedfordshireDigitalCommunications11Amplitude Modulation90

Sine Wave Review - 6ModernCommunicationsDavid GoodwinUniversity ofBedfordshireDigitalCommunications12Amplitude ModulationRemember:Sine 0 0; Sine 90 1; Sine 180 0; Sine 270 -1;Sine 360 Sine 0 090

Sine and Cosine Waves – 1ModernCommunications Sine Wave Cosine Wave shifted by 90 degreesDavid GoodwinUniversity ofBedfordshireDigitalCommunications13Amplitude Modulation90

Sine and Cosine Waves – 2ModernCommunications There is a useful java applet that will show you a sine wavederived from circular motion (simple harmonic motion)David GoodwinUniversity ofBedfordshireDigitalCommunications14Amplitude Modulation90

Sine and Cosine Waves – 3ModernCommunicationsDavid GoodwinUniversity ofBedfordshireDigitalCommunications15Amplitude Modulation90

Sine and Cosine Waves - 4ModernCommunicationsDavid GoodwinUniversity ofBedfordshireDigitalCommunications16Amplitude Modulation Sine and Cosine waves can therefore be considered to be atright angles, i.e. orthogonal, to each other90

Sine and Cosine Waves – 6ModernCommunicationsDavid GoodwinUniversity ofBedfordshireDigitalCommunications17 Any wave that is periodic (i.e. it repeats itself exactly overAmplitude Modulationsucceeding intervals) can be resolved into a number of simplesine waves, each with its own frequency This analysis of complex waveforms is part of the FourierTheorem You can build up a complex waveform with harmonics of thefundamental frequency90

ExampleModernCommunicationsDavid GoodwinUniversity ofBedfordshireDigitalCommunications18Amplitude Modulation90

ExampleModernCommunicationsDavid GoodwinUniversity ofBedfordshireDigitalCommunications19Amplitude Modulation90

Harmonics – 1ModernCommunications A harmonic is a multiple of a fundamental frequency. In theDavid GoodwinUniversity ofBedfordshireDigitalCommunications20Amplitude Modulation90figure below, a fundamental frequency of 100 Hz is shownwith 31 harmonics (total of 32 “lines”).

Harmonics – 2 In this example, 20 harmonics are mixed together to form aModernCommunicationssaw-tooth waveformDavid GoodwinUniversity ofBedfordshireDigitalCommunications21Amplitude Modulation90

Fourier series expansionModernCommunications For periodic signal we use the Fourier series expansion as aDavid GoodwinUniversity ofBedfordshireDigitalCommunicationssimple way of frequency representation of such signals22Amplitude Modulation The Fourier series expansion of a general periodic signal x(t)with period T is defined as Trigonometric expansionx(t) a0 X[an cos (2πnf0 t) bn sin (2πnf0 t)]n 1 wherea0 an bn 901TZ2TZ2TZTx(t)dt0Tx(t) cos (2πnf0 t)dt0Tx(t) sin (2πnf0 t)dt0

Transmission FundamentalsComplex Plane-Complex NumbersModernCommunications Complex plane is a two dimensional representation of complexDavid GoodwinUniversity ofBedfordshireDigitalCommunications23Amplitude Modulationnumbers and complex signals. The general definition of acomplex number z is z a jb a is the real part and b the imaginary part of z, respectivelyand j is a non-real constant such that j 2 1 simply impliesa phase difference of 90 degrees An alternative and very common representation of complexnumbers is z a jb r cos θ jr sin θ rejθ where cos θ j sin θ ejθ , r is the amplitude and θ is thephase of za2 b2 , tanθ b/a, a r cos θ, b r sin θ, r 90

Complex exponential harmonic signalModernCommunicationsDavid GoodwinUniversity ofBedfordshireDigitalCommunications x(t) ej2πf t cos (2πf t) j sin (2πf t)24 It is a very useful signal used for frequency domain analysis.Its amplitude is equal to one whereas it rotates in thecomplex plane in the counter-clockwise direction with anangular frequency ω 2πfAmplitude Modulation90

Transmission FundamentalsFrequency domain analysis-Fourier SeriesModernCommunications For periodic signal we use the Fourier series expansion as aDavid GoodwinUniversity ofBedfordshireDigitalCommunicationssimpler way of frequency representation of such signals The Fourier series expansion of a general periodic signal x(t)25with period T is defined as Trigonometric expansionAmplitude Modulationx(t) a0 X[an cos (2πnf0 t) bn sin (2πnf0 t)]n 1 Complex exponential expansion Xx(t) cn e j2πnf0 tn wherecn 1TZT /2x(t)e j2πnf0 t dt T /2 Generally, the Fourier series expansion is a simpler way ofrepresenting periodic signals90

Frequency domain analysis-Fourier TransformModernCommunications Definition of frequency content: Frequency content of a timeDavid GoodwinUniversity ofBedfordshiredomain signal is the weighed superposition of all the complexexponential harmonic signals that accurately reconstruct theinitial time domain signal. The frequency content is defined through the well-knownFourier transform FZ F [x(t)] X(f ) x(t)e j2πnf0 t dtDigitalCommunications26Amplitude Modulation The original signal can be reconstructed by its Fouriertransform through the so-called Inverse Fourier transform F 1Z x(t) F 1 [X(f )] X(f )ej2πnf0 t dt Generally, the Fourier transform is a complex valued function90having both amplitude and phase. In the above definitions,the functions x(t) and X(f) are recognized as Fouriertransform pairs

Sine and Cosine Waves - 9ModernCommunicationsDavid GoodwinUniversity ofBedfordshireDigitalCommunications27 Two conceptsAmplitude Modulation The signal may be thought of as a time varying voltage, V(t) The angle, θ, is made up of a time varying component, ωt,and a supplementary value, φ, which may be fixed or varying Thus we have a signal V (t) A cos (ωt φ)90

Sine and Cosine Waves - 10ModernCommunicationsDavid GoodwinUniversity ofBedfordshireDigitalCommunications Time varying signal28Amplitude Modulation90

Back to our Sine Wave – 1Defining the WavelengthModernCommunicationsDavid GoodwinUniversity ofBedfordshireDigitalCommunications29Amplitude Modulation90

Back to our Sine Wave - 2ModernCommunicationsDavid GoodwinUniversity ofBedfordshireDigitalCommunications30Amplitude Modulation One revolution 360 degrees One revolution also completes one cycle (or wavelength) ofthe wave. So the “phase” of the wave has moved from 0 degrees to 360degrees (i.e. back to 0 degrees ) in one cycle.The faster thephase changes, the shorter the time one cycle (onewavelength) takes90

Back to our Sine Wave – 3Two useful equationsModernCommunicationsDavid GoodwinUniversity ofBedfordshireDigitalCommunications31Amplitude Modulation The time taken to complete one cycle, or wavelength, is theperiod, T. Frequency is the reciprocal of the period, that is f 1T Phase has changed by θ The rate-of-change of the phase,90dθ, is the frequency, f.dt

Sine Wave – 4ModernCommunications What do we mean “Rate-of-change of phase is frequency”?David GoodwinUniversity ofBedfordshireDigitalCommunications One revolution 360 degrees 2π radians 1 cycle32 One revolution/s 1 cycle/s 1 Hz Examples:Amplitude Modulation 720 degrees/s 2 revolutions/s 2 Hz 18,000 degrees/s 18,000/360 revs/s 50 revs/s 50 Hz90

Simple Harmonic MotionModernCommunicationsDavid GoodwinUniversity ofBedfordshireDigitalCommunications33Amplitude Modulation Geometric derivation of simple harmonic motion. A point pmoves at constant speed on the circumference of a circle incounter-clockwise motion. Its projection OC on the verticalaxis XOY is shown at right as a function of the angle θ. Thefunction described is that of a sine wave.90

Sine Wave ContinuedModernCommunicationsDavid GoodwinUniversity ofBedfordshireDigitalCommunications Can think of a Sine Wave as a Carrier Signal, i.e. the signal34Amplitude Modulation90onto which the information is loaded for sending to the enduser A Carrier Signal is used as the basis for sendingelectromagnetic signals between a transmitter and a receiver,independently of the frequency

Carrier signals - 1ModernCommunicationsDavid GoodwinUniversity ofBedfordshireDigitalCommunications A Carrier Signal may be considered to travel at the speed of35light, c, whether it is in free space or in a metal wire Travels more slowly in most substancesAmplitude Modulation The velocity, frequency, and wavelength of the carrier signalare uniquely connected byc fλ where: c velocity of light (m/s) f frequency (1/s, Hz) λ wavelength (m)90

Carrier signals - 2ModernCommunicationsDavid GoodwinUniversity ofBedfordshireDigitalCommunications36 Example WAMU (National Public Radio) transmits at a carrierAmplitude Modulationfrequency of 88.5 MHz What is the wavelength of the carrier signal? Answer: c (3 108 )m/s f λ (88.5 106 ) (λ) Which gives λ 3.3898 3.4 m Remember: Make sure you are using the correct units90

Transmission FundamentalsWhy Digital Communications?ModernCommunications Analog TransmissionDavid GoodwinUniversity ofBedfordshireDigitalCommunications Each repeater attempts to restore analog signal to its original37form Restoration is imperfectAmplitude Modulation Distortion is not completely eliminated Noise & interference is only partially removed Signal quality decreases with number of repeaters Communications is distance-limited Still used in analog cable TV systems90

Transmission FundamentalsWhy Digital Communications?ModernCommunicationsDavid GoodwinUniversity ofBedfordshireDigitalCommunications Digital Transmission38 Regenerator recovers original data sequence and retransmitson next segment Then each regeneration is like transmitting for first time! Communications is possible over very long distances Digital systems vs. analog systemsAmplitude Modulation Less power, longer distances, lower system cost Monitoring, multiplexing, coding, encryption, protocols. . .90

Transmission FundamentalsWhy Digital Communications?ModernCommunications Analog transmission: all details must be reproducedaccuratelyDavid GoodwinUniversity ofBedfordshireDigitalCommunications39Amplitude Modulation Analog transmission: all details must be reproducedaccurately90 Simpler Receiver: Was original pulse positive or negative?