1. Transmission Media

2. Quiz: ANGEL->Lessons->Quiz 2 Figure 1Figure 2 Figure 3Figure 4

3. Reading for next class Ch. 8.1 – 8.12

4. 4 Review: Bandwidth of a digital signal The bandwidth of a digital signal is infinite! – Accurate representation of a digital signal requires an infinite set of sine waves. – Transmitting/reproducing digital signals is impractical

5. 5 Review: Bandwidth-Limited Signals The bandwidth of a digital signal is infinite! – Accurate representation of a digital signal requires an infinite set of sine waves. – Transmitting/reproducing digital signals is impractical Engineers adopt a compromise: – generate composite sine waves that closely approximate the digital signal – the quality of approximation depends on the channel bandwidth

6. Review: Bandwidth-Limited Signals Having less bandwidth degrades the signal 8 sine waves 4 sine waves 2 sine waves Lost! Bandwidth Lost!

7. 7 Receiver: Converting an Analog Signal back to Digital 1.(Sampling) The level of analog signal is measured repeatedly at fixed time intervals 2.(Quantization) A sample is then quantized by converting it into an integer value…

8. How many samples do we need? 8 too few samples: may only give a crude approximation of the original signal too many samples: more digital data will be generated, which uses extra bandwidth

9. 9 The Nyquist Theorem and Sampling Rate A mathematician named Nyquist discovered exactly how much sampling is required: – f max : the highest frequency in the composite signal. Sample a signal at least twice as fast as the highest frequency that must be preserved.

10. Example: At what rate should we sample this signal? Maximum frequency = 2Hz Sampling rate: 2*2Hz = 4Hz

11. Exercise Q: At what rate should we sample the following signal?

12. Bandwidth to Channel Capacity In practice, the maximum frequency of a signal is determined by the channel bandwidth B. – Nyquist Theorem: maximum symbol rate (baud) is 2B Thus, if there are K signal levels, ignoring noise, the maximum bit rate is:

13. 13 Example: Bit Rate of Telephone System Audio bandwidth – Acceptable quality: preserving frequency up to 4k – Sampling rate (baud) = 2*4K = 8K Quantization: – Reasonable quality reproduction: 8 bits / 256 levels

14. Exercise If 8 signal levels are used, what is the data rate that can be sent over a coaxial cable that has an analog bandwidth of 6.2 MHz?

15. A Taxonomy of Transmission Media by Forms of Energy. wired

16. Twisted Pair, Coaxial Cable, or Optical Fiber? Figure 1Figure 2 Figure 3Figure 4

17. . Copper (Electrical) Wiring vs. Optical Fiber Copper – Less expensive – No need special treatment on wires Ends of an optical fiber must be polished before being used. – Installation is easy. – Less likely to break if accidentally pulled or bent Optical fiber – Immune to electrical noise – Higher bandwidth – Light traveling across a fiber does not attenuate as much as electrical signals traveling across copper.

18. How fast can we send information over a channel with noise? Key channel properties: The bandwidth (B), single strength (S), and noise strength (N) – B limits the rate of transmissions – S and N limit how many signal levels we can distinguish Bandwidth B Signal S, Noise N

19. The Effect of Noise on Communication In practice, the signal levels we can distinguish depends on S/N – Or SNR, the Signal-to-Noise Ratio Shannon’s Theorem

20. Example If a system has an average power level of 100, an average noise level of 33.33, and a bandwidth of 100 MHz, what is the effective limit on channel capacity?

21. Calculate Channel Capacity with S/N in dB SNR often given on a log-scale in deciBels: Example: the voice telephone system: – Signal-to-noise ratio: about 30 dB – An analog bandwidth: about 3 kHz Calculation – Step 1: Converting the S/N in dB into a simple fraction: S/N = 10 (dB/10) 30dB  1000 – Step 2: Applying Shannon's Theorem about 30,000 bps dB = 10log 10 (S/N)

22. Exercise If a telephone system can be created with a signal-to-noise ratio of 40 dB and an analog bandwidth of 3000 Hz, how many bits per second could be transmitted?