1. Chapter 2 Signal Analysis & Transmission via Channel

2. Chapter overview Periodic and Transient signals Communication Signals & Their Characteristics Noise in Communication Systems Signal Transmission

3. Periodic and Transient Signals Introduction –Signals – any sign, gesture or token that serves to communicate information. –Applied in electronics communications – Signal implies an electrical quantity (e.g. voltage) possessing some characteristic (e.g. amplitude) which varies unpredictably.

4. Cont’d... Waveform – the shape of a wave oscillation obtained by plotting the value of some changing quantity against time. –In electronic communications – waveform implies an electrical quantity which varies periodically and therefore predictably. –Waveform can be adapted to convey information by varying its parameters in sympathy with a signal (e.g. sinusoid carrier )

5. Cont’d... Periodic signals –Shifted by an appropriate time interval is unchanged. –Synonymous with waveform –Example : A periodic signal

6. Cont’d... A signal f(t) is called periodic in time if there exists a constant T 0 > 0 : for -∞ < t < ∞ The smallest value of T 0 that satisfies this condition is called the period of f(t) –T 0 = The duration of one complete cycle of f(t)

7. Cont’d... Normalized power, P averaged over any T second period is: Total energy, E in a periodic signal is:

8. Example Find the average normalized power in the waveform, x(t) = A cos 2Пf 0 t using time averaging.

9. Cont’d... Transient signals –One which has a well defined location in time. –Does not necessarily mean it must be zero outside a certain time interval –The signals tends to 0 as time tends to ±∞ –Energy signals –Can ’ t be represented by an ordinary FS – Aperiodic.

10. Cont’d... Fourier Transform –Traditional way of approaching FT – treat them as a limiting case of a periodic signal Fourier series as T tends to infinity. –Example : Pulse periodic waveform with interpulse spacing T g

11. Cont’d... Sufficient conditions for the existence of a FT –v(t) contains a finite number of maxima and minima in any finite time interval –v(t) contains a finite number of finite discontinuities in any finite time interval –v(t) must be absolutely intergrable:

12. Cont’d... Symmetry properties of FT FunctionTransform Real and even Real and oddImaginary and odd Imaginary and even Imaginary and oddReal and odd Complex and even Complex and odd Real even plus imaginary odd Real Real odd plus imaginary even Imaginary Even Odd

13. Communication Channels & Their Characteristics Provides the connection between the transmitter and receiver. –Pair of wires – carry electric signal. –Optical fiber – carries the information on a modulated light beam. –Free space – information-bearing signal is radiated by antenna

14. Cont’d... Signal transmission problem –additive noise – generated internally by components used to implement the communication system. –Interference from other users of the channel.

15. Cont’d... Minimizing noise effects - Increasing the power of transmitted signal. Constraint –Limited power level –Channel bandwidth availability

16. Cont’d... Channels Wire lines Wireless electromagnetic Fiber optics Underwater acoustic

17. Cont’d... Wire Lines Channel –Signals transmitted are distorted in both amplitude and phase – corrupted by noise –Carry a large percentage of daily communication around the world http://en.wikipedia.org/wiki/Coaxial_cable http://en.wikipedia.org/wiki/Twisted_pair Coaxial cable Twisted pair

18. Cont’d... Fiber Optics Channel –Low signal attenuation –Highly reliable photonic devices –Large bandwidth available –Services : voice, data facsimile and video –Tx – light source (e.g. LED, laser) –Rx – photodiode –Noise source : photodiodes & amplifiers http://en.wikipedia.org/wiki/Fiber_optics

19. Cont’d... Wireless Electromagnetic Channels –Electromagnetic energy is coupled to the propagation medium by antenna (radiator) –Antenna size & configuration – Frequency of operation –Efficient radiation – antenna longer than 1/10 λ

20. Cont’d... Example A radio station transmitting in AM frequency band, f c = 1MHz, λ = 300 m, requires antenna at least 30 m.

21. Cont’d... Various frequency bands of the electromagnetic spectrum

22. Cont’d... Mode of propagation of EM waves i.Ground-wave propagation ii.Sky-wave propagation iii.Line-of-sight (LOS)

23. GROUND-WAVE PROPAGATION Surface-wave propagation Dominant mode of propagation Frequency band: 0.3 – 3 MHz Applications: AM broadcasting, maritime radio broadcasting Disturbances for signal transmission: atmospheric noise, man-made noise, thermal noise

24. Cont’d...

25. SKY-WAVE PROPAGATION Transmitted signals being reflected from ionosphere Frequency : above 30 MHz Little loss Problem : Signal Multipath Application : Satellite communications

26. Cont’d... Antenna at different angles > f c

27. LINE-OF-SIGHT (LOS) PROPAGATION VHF band and higher Limited by curvature of earth Problem : Thermal noise (Rx front end) Cosmic noise (pick-up by antenna) Application: A TV antenna mounted on a tower of 300 m height to provide a broad coverage area (67km)

28. Cont’d...

29. Underwater acoustic channels –EM waves do not propagate over long distances under water except at extremely low frequencies –Expensive – because of the large and powerful transmitters required –Problem : Attenuation – skin depth

30. Cont’d... Multipath channel – signals reflections from the surface and the bottom of the sea. Noise : ambient ocean acoustic noise, man-made acoustic noise

31. Noise in Communication System

32. Cont’d... Define as undesired random variations that interface with the desired signal and inhibit communication. Where does noise originate in a communication system? Channel @ transmission medium Devices @ Equipments Noise Effect One of the main limiting factor in obtaining high performance of a communication system. Decrease the quality of the receiving signal.

33. Cont’d... Man-made noise –Spark-plug ignition noise, switching transient or other radiating electromagnetic signals. Natural noise –Atmosphere, sun or other galactic sources.

34. Cont’d... Solution : filtering, shielding, modulation choice, Rx selection Example : sensitive radio astronomy measurements are located at remote desert locations –Far from man-made noise –Can’t avoid the natural noise source – thermal or Johnson noise

35. Cont’d... Thermal noise –A zero mean Gaussian random process –A Gaussian process n(t) is a random function whose value n at any arbitrary time t is statistically characterized by the Gaussian probability density function Where σ² the variance of n

36. –Normalized Gaussian density function,σ =1 –Represent a random signal as the sum of a Gaussian noise random variable and a dc signal. where z is random signal a is dc component n is the Gaussian noise random variable

37. Cont’d... The pdf p(z) is expressed as Gaussian distribution is often used as the system noise model –Central limit theorem

38. Cont’d... White noise –Useful abstraction – no noise process can truly be white but approximately white –Noise observation after it has pass through a real system – finite bandwidth –Effect on the detection process of a channel with AWGN – noise affects each transmitted symbol independently Additive : the noise is simply superimposed or added to the signal – that there are no multiplicative mechanism at work.

39. Cont’d... A simple model assumes that power spectral density G n (f) is flat for all frequencies. The autocorrelation function of white noise is given by the inverse FT of the noise power spectral density. Average power P n of white noise is infinite because its BW is infinite.

40. Cont’d... a) Power spectral density of WN b) Autocorrelation function of WN

41. Noise power and noise voltage in circuit with R L Noise voltage across a load, R L (V n )² = 4KTBWR L Noise power P = KTBW

42. Cont’d... Example Determine the noise voltage and noise power for the given circuit with operating temperature of 330 K and bandwidth of 20 MHz.

43. Signal Transmission Signal transmission through linear system System can be characterized equally well in the time domain or frequency domain. Linear system with its key parameters Linear network Input Output x(t) h(t) y(t) X(f) H(f) Y(f)

44. Cont’d... The input signal can be described as a time domain signal x(t) or by its FT, X(f). Time domain analysis yields the time domain output y(t) and in the process, h(t), the impulse response of the network will be defined. If the input is in frequency domain, the frequency transfer function H(f) will determine the frequency domain output Y(f). The system assumed to be linear & time invariant and there is no stored energy in the system at the time input is applied.

45. Cont’d... Distortionless Transmission –The output signal from an ideal transmission line may have time delay – different amplitude –To achieve Ideal distortionless transmission, the overall system response must have Constant magnitude response Phase shift must be linear (proportional) with frequency Identical time delay Textbook page 35, 36, 37

46. END OF CHAPTER 2