1 / 84

COE 342: Data & Computer Communications (T042) Dr. Marwan Abu-Amara

Explore key concepts and terminology in data transmission, including decibels, Fourier analysis, analog vs. digital signals, transmission impairments, and channel capacity in the realm of computer communications. Learn about signal strength, periodic vs. aperiodic signals, frequency domains, and bandwidth considerations.

ehardeman
Download Presentation

COE 342: Data & Computer Communications (T042) 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 342: Data & Computer Communications (T042)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 342 (T042) – 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 342 (T042) – 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 342 (T042) – 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 342 (T042) – 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 342 (T042) – Dr. Marwan Abu-Amara

  7. Analogue & Digital Signals COE 342 (T042) – Dr. Marwan Abu-Amara

  8. PeriodicSignals COE 342 (T042) – Dr. Marwan Abu-Amara

  9. Sine Wave • Peak Amplitude (A) • maximum strength of signal • volts • Frequency (f) • Rate of change of signal • Hertz (Hz) or cycles per second • Period = time for one repetition (T) • T = 1/f • Phase () • Relative position in time COE 342 (T042) – Dr. Marwan Abu-Amara

  10. Varying Sine Wavess(t) = A sin(2ft +) COE 342 (T042) – 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 • c = 3*108 m/sec(speed of light in free space) COE 342 (T042) – 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 342 (T042) – Dr. Marwan Abu-Amara

  13. Addition of FrequencyComponents(T=1/f) COE 342 (T042) – Dr. Marwan Abu-Amara

  14. FrequencyDomainRepresentations COE 342 (T042) – 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 342 (T042) – Dr. Marwan Abu-Amara

  16. 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 342 (T042) – Dr. Marwan Abu-Amara

  17. 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 342 (T042) – Dr. Marwan Abu-Amara

  18. Relationship Between Decibel Values and Powers of 10 COE 342 (T042) – Dr. Marwan Abu-Amara

  19. 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 342 (T042) – Dr. Marwan Abu-Amara

  20. 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 342 (T042) – Dr. Marwan Abu-Amara

  21. 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 342 (T042) – Dr. Marwan Abu-Amara

  22. Fourier Series • Any periodic signal 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 342 (T042) – Dr. Marwan Abu-Amara

  23. Fourier Series • Amplitude-phase representation COE 342 (T042) – Dr. Marwan Abu-Amara

  24. COE 342 (T042) – Dr. Marwan Abu-Amara

  25. 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 342 (T042) – Dr. Marwan Abu-Amara

  26. Fourier Series Representation of Periodic Signals - Example Replacing t by –t in the first integral sin(-2pnf t)= - sin(2pnf t) COE 342 (T042) – Dr. Marwan Abu-Amara

  27. 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, … COE 342 (T042) – Dr. Marwan Abu-Amara

  28. Another Example 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 342 (T042) – Dr. Marwan Abu-Amara

  29. Another Example COE 342 (T042) – Dr. Marwan Abu-Amara

  30. 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. • Spectrum can be defined by Fourier transform • For a signal x(t) with spectrum X(f), the following relations hold COE 342 (T042) – Dr. Marwan Abu-Amara

  31. COE 342 (T042) – Dr. Marwan Abu-Amara

  32. Fourier Transform Example x(t) A COE 342 (T042) – Dr. Marwan Abu-Amara

  33. Fourier Transform Example COE 342 (T042) – Dr. Marwan Abu-Amara

  34. Signal Power • A function x(t) specifies a signal in terms of either voltage or current • Instantaneous power of a signal is related to average power of a time-limited signal, and is defined as • For a periodic signal, the average power in one period is COE 342 (T042) – Dr. Marwan Abu-Amara

  35. Power Spectral Density & Bandwidth • Absolute bandwidth of any time-limited signal is infinite. • Most power in a signal is concentrated in finite band. • Effective bandwidth is the spectrum portion containing most of the power. • Power spectral density (PSD) describes power content of a signal as a function of frequency COE 342 (T042) – Dr. Marwan Abu-Amara

  36. Power Spectral Density & Bandwidth • For a periodic signal, power spectral density is where (f) is COE 342 (T042) – Dr. Marwan Abu-Amara

  37. 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 342 (T042) – Dr. Marwan Abu-Amara

  38. Power Spectral Density & Bandwidth - Example • Consider the following signal • The signal power is COE 342 (T042) – Dr. Marwan Abu-Amara

  39. 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) • Find the total power of s(t) • Find a value of n such that Fourier series for s(t) contains 95% of the total power in the original signal • Write an expression for the power spectral density function for s(t) COE 342 (T042) – Dr. Marwan Abu-Amara

  40. Example (Cont.) • Mathematical expression for s(t): COE 342 (T042) – Dr. Marwan Abu-Amara

  41. Example (Cont.) • Fourier Analysis: COE 342 (T042) – Dr. Marwan Abu-Amara

  42. Example (Cont.) • Fourier Analysis (cont.): COE 342 (T042) – Dr. Marwan Abu-Amara

  43. Example (Cont.) • Fourier Analysis (cont.): COE 342 (T042) – Dr. Marwan Abu-Amara

  44. Example (Cont.) • Fourier Analysis (cont.): COE 342 (T042) – Dr. Marwan Abu-Amara

  45. Example (Cont.) • Fourier Analysis (cont.): COE 342 (T042) – Dr. Marwan Abu-Amara

  46. Example (Cont.) • Fourier Analysis (cont.): COE 342 (T042) – Dr. Marwan Abu-Amara

  47. Example (Cont.) • Fourier Analysis (cont.): COE 342 (T042) – Dr. Marwan Abu-Amara

  48. Example (Cont.) • Total Power: COE 342 (T042) – Dr. Marwan Abu-Amara

  49. Example (Cont.) • Finding n such that we get 95% of total power: COE 342 (T042) – Dr. Marwan Abu-Amara

  50. Example (Cont.) • Finding n such that we get 95% of total power: COE 342 (T042) – Dr. Marwan Abu-Amara

More Related