1 / 101

COE 341: Data & Computer Communications (T081) Dr. Marwan Abu-Amara

COE 341: Data & Computer Communications (T081) Dr. Marwan Abu-Amara. Chapter 3: Data Transmission. Agenda. Concepts & Terminology Decibels and Signal Strength Fourier Analysis Analog & Digital Data Transmission Transmission Impairments Channel Capacity. Terminology (1). Transmitter

denise-conway
Download Presentation

COE 341: Data & Computer Communications (T081) Dr. Marwan Abu-Amara

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. COE 341: Data & Computer Communications (T081)Dr. Marwan Abu-Amara Chapter 3: Data Transmission

  2. Agenda • Concepts & Terminology • Decibels and Signal Strength • Fourier Analysis • Analog & Digital Data Transmission • Transmission Impairments • Channel Capacity COE 341 – Dr. Marwan Abu-Amara

  3. Terminology (1) • Transmitter • Receiver • Medium • Guided medium • e.g. twisted pair, optical fiber • Unguided medium • e.g. air, water, vacuum COE 341 – Dr. Marwan Abu-Amara

  4. Terminology (2) • Direct link • No intermediate devices • Point-to-point • Direct link • Only 2 devices share link • Multi-point • More than two devices share the link COE 341 – Dr. Marwan Abu-Amara

  5. Terminology (3) • Simplex • One direction • e.g. Television • Half duplex • Either direction, but only one way at a time • e.g. police radio • Full duplex • Both directions at the same time • e.g. telephone COE 341 – Dr. Marwan Abu-Amara

  6. Frequency, Spectrum and Bandwidth • Time domain concepts • Analog signal • Varies in a smooth way over time • Digital signal • Maintains a constant level then changes to another constant level • Periodic signal • Pattern repeated over time • Aperiodic signal • Pattern not repeated over time COE 341 – Dr. Marwan Abu-Amara

  7. Analogue & Digital Signals COE 341 – Dr. Marwan Abu-Amara

  8. T PeriodicSignals Temporal Period S (t+nT) = S (t); Where: t is time T is the waveform period n is an integer COE 341 – Dr. Marwan Abu-Amara

  9. Sine Wave – s(t) = A sin(2ft +) • Peak Amplitude (A) • maximum strength of signal • unit: volts • Frequency (f) • rate of change of signal • unit: Hertz (Hz) or cycles per second • Period = time for one repetition (T) = 1/f • Phase () • relative position in time • unit: radians • Angular Frequency (w) • w = 2 /T = 2 f • unit: radians per second COE 341 – Dr. Marwan Abu-Amara

  10. Varying Sine Wavess(t) = A sin(2ft +) COE 341 – Dr. Marwan Abu-Amara

  11. Wavelength () • Distance occupied by one cycle • Distance between two points of corresponding phase in two consecutive cycles • Assuming signal velocity v •  = vT • f = v • For an electromagnetic wave, v = speed of light in the medium • In free space, v = c = 3*108 m/sec COE 341 – Dr. Marwan Abu-Amara

  12. Frequency Domain Concepts • Signal usually made up of many frequencies • Components are sine waves • Can be shown (Fourier analysis) that any signal is made up of component sine waves • Can plot frequency domain functions COE 341 – Dr. Marwan Abu-Amara

  13. Addition of FrequencyComponents(T=1/f) Fundamental Frequency COE 341 – Dr. Marwan Abu-Amara

  14. FrequencyDomainRepresentations COE 341 – Dr. Marwan Abu-Amara

  15. Spectrum & Bandwidth • Spectrum • range of frequencies contained in signal • Absolute bandwidth • width of spectrum • Effective bandwidth • Often just bandwidth • Narrow band of frequencies containing most of the energy • DC Component • Component of zero frequency COE 341 – Dr. Marwan Abu-Amara

  16. Signal with a DC Component t 1V DC Level t 1V DC Component COE 341 – Dr. Marwan Abu-Amara

  17. Bandwidth for these signals: COE 341 – Dr. Marwan Abu-Amara

  18. Bandwidth and Data Rate • Any transmission system supports only a limitedband of frequencies for satisfactory transmission • “system” includes: TX, RX, and Medium • Limitation is dictated by considerations of cost, number of channels, etc. • This limitedbandwidth degrades the transmitted signals, making it difficult to interpret them at RX • For a given bandwidth: Higher data rates More degradation • This limits the data rate that can be used withgiven signal and noise levels, receiver type, and error performance • More about this later!!! COE 341 – Dr. Marwan Abu-Amara

  19. Bandwidth Requirements 1,3 Larger BW needed for better representation BW = 2f More difficult reception with more limited BW f 3f 1 1,3,5 BW = 4f 5f f 3f 2 1,3,5,7 BW = 6f 7f 5f f 3f 3 … BW =  1,3,5,7 ,9,… COE 341 – Dr. Marwan Abu-Amara ……  7f 5f f 3f 4 Fourier Series for a Square Wave

  20. Decibels and Signal Strength • Decibel is a measure of ratio between two signal levels • NdB= number of decibels • P1 = input power level • P2 = output power level • Example: • A signal with power level of 10mW inserted onto a transmission line • Measured power some distance away is 5mW • Loss expressed as NdB =10log(5/10)=10(-0.3)=-3 dB COE 341 – Dr. Marwan Abu-Amara

  21. Decibels and Signal Strength • Decibel is a measure of relative, not absolute, difference • A loss from 1000 mW to 500 mW is a loss of 3dB • A loss of 3 dB halves the power • A gain of 3 dB doubles the power • Example: • Input to transmission system at power level of 4 mW • First element is transmission line with a 12 dB loss • Second element is amplifier with 35 dB gain • Third element is transmission line with 10 dB loss • Output power P2 • (-12+35-10)=13 dB = 10 log (P2 / 4mW) • P2 = 4 x 101.3 mW = 79.8 mW COE 341 – Dr. Marwan Abu-Amara

  22. Relationship Between Decibel Values and Powers of 10 COE 341 – Dr. Marwan Abu-Amara

  23. Decibel-Watt (dBW) • Absolute level of power in decibels • Value of 1 W is a reference defined to be 0 dBW • Example: • Power of 1000 W is 30 dBW • Power of 1 mW is –30 dBW COE 341 – Dr. Marwan Abu-Amara

  24. Decibel & Difference in Voltage • Decibel is used to measure difference in voltage. • Power P=V2/R • Decibel-millivolt (dBmV) is an absolute unit with 0 dBmV equivalent to 1mV. • Used in cable TV and broadband LAN COE 341 – Dr. Marwan Abu-Amara

  25. Fourier Analysis Signals Aperiodic Periodic (fo) Discrete Continuous Discrete Continuous DFS FS FT Finite time Infinite time DTFT DFT FT : Fourier Transform DFT : Discrete Fourier Transform DTFT : Discrete Time Fourier Transform FS : Fourier Series DFS : Discrete Fourier Series COE 341 – Dr. Marwan Abu-Amara

  26. Fourier Series (Appendix B) • Any periodic signal of period T (f0 = 1/T) can be represented as sum of sinusoids, known as Fourier Series fundamental frequency DC Component If A0 is not 0, x(t) has a DC component COE 341 – Dr. Marwan Abu-Amara

  27. Fourier Series • Amplitude-phase representation COE 341 – Dr. Marwan Abu-Amara

  28. COE 341 – Dr. Marwan Abu-Amara

  29. Fourier Series Representation of Periodic Signals - Example x(t) 1 -3/2 -1 -1/2 1/2 1 3/2 2 -1 T Note: (1) x(– t)=x(t)  x(t) is an even function (2) f0 = 1 / T = ½ COE 341 – Dr. Marwan Abu-Amara

  30. Fourier Series Representation of Periodic Signals - Example Replacing t by –t in the first integral sin(-2pnf t)= - sin(2pnf t) COE 341 – Dr. Marwan Abu-Amara

  31. Fourier Series Representation of Periodic Signals - Example Since x(– t)=x(t) as x(t) is an even function, then Bn = 0 for n=1, 2, 3, … Cosine is an even function COE 341 – Dr. Marwan Abu-Amara

  32. Another Example x(t) x1(t) 1 -2 -1 1 2 -1 T Note that x1(-t)= -x1(t)  x(t) is an odd function Also, x1(t)=x(t-1/2) COE 341 – Dr. Marwan Abu-Amara

  33. Another Example Sine is an odd function Where: COE 341 – Dr. Marwan Abu-Amara

  34. Fourier Transform • For a periodic signal, spectrum consists of discrete frequency components at fundamental frequency & its harmonics. • For an aperiodic signal, spectrum consists of a continuum of frequencies (non-discrete components). • Spectrum can be defined by Fourier Transform • For a signal x(t) with spectrum X(f), the following relations hold COE 341 – Dr. Marwan Abu-Amara

  35. COE 341 – Dr. Marwan Abu-Amara

  36. Fourier Transform Example x(t) A COE 341 – Dr. Marwan Abu-Amara

  37. A   t f  1/ Fourier Transform Example Sin (x) / x “sinc” function COE 341 – Dr. Marwan Abu-Amara Study the effect of the pulse width 

  38. The narrower a function is in one domain, the wider its transform is in the other domain The Extreme Cases COE 341 – Dr. Marwan Abu-Amara

  39. Power Spectral Density & Bandwidth • Absolute bandwidth of any time-limited signal is infinite • However, most of the signal power will be concentrated in a finite band of frequencies • Effective bandwidth is the width of the spectrum portion containing most of the signal power. • Power spectral density (PSD) describes the distribution of the power content of a signal as a function of frequency COE 341 – Dr. Marwan Abu-Amara

  40. Signal Power • A function x(t) specifies a signal in terms of either voltage or current • Assuming R = 1 W, Instantaneous signal power = V2 = i2 = |x(t)|2 • Instantaneous power of a signal is related to average power of a time-limited signal, and is defined as • For a periodic signal, the averaging is taken over one period to give the total signal power COE 341 – Dr. Marwan Abu-Amara

  41. Power Spectral Density & Bandwidth • For a periodic signal, power spectral density is where (f) is Cn is as defined before on slide 27, and f0 being the fundamental frequency COE 341 – Dr. Marwan Abu-Amara

  42. Power Spectral Density & Bandwidth • For a continuous valued function S(f), power contained in a band of frequencies f1 < f < f2 • For a periodic waveform, the power through the first j harmonics is COE 341 – Dr. Marwan Abu-Amara

  43. Power Spectral Density & Bandwidth - Example • Consider the following signal • The signal power is COE 341 – Dr. Marwan Abu-Amara

  44. Fourier Analysis Example • Consider the half-wave rectified cosine signal from Figure B.1 on page 793: • Write a mathematical expression for s(t) • Compute the Fourier series for s(t) • Write an expression for the power spectral density function for s(t) • Find the total power of s(t) from the time domain • Find a value of n such that Fourier series for s(t) contains 95% of the total power in the original signal • Determine the corresponding effective bandwidth for the signal COE 341 – Dr. Marwan Abu-Amara

  45. +3T/4 +T/4 -3T/4 -T/4 Example (Cont.) • Mathematical expression for s(t): Where f0 is the fundamental frequency, f0 = (1/T) COE 341 – Dr. Marwan Abu-Amara

  46. Example (Cont.) f0 = (1/T) • Fourier Analysis: COE 341 – Dr. Marwan Abu-Amara

  47. Example (Cont.) f0 = (1/T) • Fourier Analysis (cont.): COE 341 – Dr. Marwan Abu-Amara

  48. Example (Cont.) • Fourier Analysis (cont.): COE 341 – Dr. Marwan Abu-Amara

  49. Example (Cont.) • Fourier Analysis (cont.): Note: cos2q = ½(1 + cos 2q) COE 341 – Dr. Marwan Abu-Amara

  50. Example (Cont.) • Fourier Analysis (cont.): COE 341 – Dr. Marwan Abu-Amara

More Related