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Datornätverk A – lektion 4 MKS B – lektion 4

Datornätverk A – lektion 4 MKS B – lektion 4 . Kapitel 5: Modulation. 4.3 Sampling. Pulse Amplitude Modulation Pulse Code Modulation Sampling Rate: Nyquist Theorem How Many Bits per Sample? Bit Rate. AD-omvand- lare med seriell utsignal. DA- omvandlare. Interpola- tionsfilter.

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Datornätverk A – lektion 4 MKS B – lektion 4

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  1. Datornätverk A – lektion 4MKS B – lektion 4 Kapitel 5: Modulation.

  2. 4.3 Sampling Pulse Amplitude Modulation Pulse Code Modulation Sampling Rate: Nyquist Theorem How Many Bits per Sample? Bit Rate

  3. AD-omvand- lare med seriell utsignal DA- omvandlare Interpola- tionsfilter Antiviknings- filter Sampler 8 bit per sampel dvs 64000 bps per tfnsamtal 28 = 256spänningsnivåer PCM = Pulse Code Modulation = Digitalisering av analoga signaler och seriell överföring Sifferexempel från PSTN = publika telefonnätet: 011011010001... 1 0 Högtalare Mikrofon 8000 sampels per sek 3400- 4000Hz filter

  4. Exempel En 6 sekunder lång ljudinspelning digitaliseras. Hur stor är inspelningens informationsmängd? a) 22000 sampels/sekund, 256 kvantiseringsnivåer. b) 22000 sampels/sekund, 16 kvantiseringsnivåer. c) 5500 sampels/sekund, 256 kvantiseringsnivåer. 22000sampels * 6 s * 8 bit = 1056000bit. • 22000sampels * 6 s * 4 bit = 528000bit. 5500sampels * 6 s * 8 bit = 264000bit.

  5. f < fs/2 Den högsta frekvens som kan samplas är halva samplingsfrekvensen. Om man samplar högre frekvens än fs/2 så byter signalen frekvens, dvs det uppstår vikningsdistorsion (aliasing). För att undvika vikningsdistorsion så har man ett anti-vikningsfilter innan samplingen, som tar bort frekvenser över halva samplingsfrekvensen. Interpolationsfiltret används vid rekonstruktion av den digitala signalen för att ”gissa” värden mellan samplen. Ett ideal interpolationsfilter skulle kunna återskapa den samplade signalen perfekt om den uppfyller samplingsteoremet. I verkligheten finns inga ideala filter. Följdregel: Nyqvist’s sats säger att max datahastighet = 2B2log M, där M är antal nivåer, och B är signalens bandbredd, oftast lika med signalens övre gränsfrekvens. Samplingsteoremet

  6. Figure 4.18PAM

  7. Note: Pulse amplitude modulation has some applications, but it is not used by itself in data communication. However, it is the first step in another very popular conversion method called pulse code modulation.

  8. Figure 4.19Quantized PAM signal

  9. Figure 4.20Quantizing by using sign and magnitude

  10. Note: According to the Nyquist theorem, the sampling rate must be at least 2 times the highest frequency.

  11. Example 4 What sampling rate is needed for a signal with a bandwidth of 10,000 Hz (1000 to 11,000 Hz)? Solution The sampling rate must be twice the highest frequency in the signal: Sampling rate = 2 x (11,000) = 22,000 samples/s

  12. Example 5 A signal is sampled. Each sample requires at least 12 levels of precision (+0 to +5 and -0 to -5). How many bits should be sent for each sample? Solution We need 4 bits; 1 bit for the sign and 3 bits for the value. A 3-bit value can represent 23 = 8 levels (000 to 111), which is more than what we need. A 2-bit value is not enough since 22 = 4. A 4-bit value is too much because 24 = 16.

  13. Example 6 We want to digitize the human voice. What is the bit rate, assuming 8 bits per sample? Solution The human voice normally contains frequencies from 0 to 4000 Hz. Sampling rate = 4000 x 2 = 8000 samples/s Bit rate = sampling rate x number of bits per sample = 8000 x 8 = 64,000 bps = 64 Kbps

  14. Distorsion till följd av digitalisering • Vikningsdistorsion • Inträffar om man inte filtrerar bort frekvenser som är högre än halva samplingsfrekvensen. • Kvantiseringsdistorsion (kvantiseringsbrus) • Avrundningsfelet låter ofta som ett brus. • Varje extra bit upplösning ger dubbelt så många spänningsnivåer, vilket ger en minskning av kvantiseringsdistorsionen med 6 dB. 16 bit upplösning ger ett signal-brus-förhållande på ca 16*6 = 96 dB (beroende på hur man mäter detta förhållande.) • Svaga ljud avrundas bort, eller dränks i kvantiseringsbruset.

  15. Informationsmängd • N bit kan representera 2N alternativa värden eller koder. Ex: ASCII-kodens 7 bitar kan representera 27 = 2·2 ·2 ·2 ·2 ·2 ·2 = 128 tecken. • En kod som kan anta M alternativa värden har informationsmängden Ex: ISO-latinkodens 256 tecken kräver 2log 256 = 8 bit per tecken.

  16. Figure 5.25Types of analog-to-analog modulation

  17. Figure 5.26Amplitude modulation

  18. Figure 5.29Frequency modulation

  19. Modulation och demodulation • Baudrate = antal symboler per sekund. Enhet: baud eller symboler/sekund. • Bitrate = datahastighet. Enhet: bps eller bit/s. • Vid många modulationsformer t.ex. s.k. ASK, PSK, och QAM är signalens bandbredd = symbolhastigheten. • Vid FSK är bandbredden vanligen större.

  20. Digitala modulationsmetoder Binär signal ASK = Amplitude Shift Keying (AM) FSK = Frequency Shift Keying (FM) PSK = Phase Shift Keying (PSK)

  21. 00 1 0 -1 0 0.5 1 time [milliseconds] 01 1 0 -1 0 0.5 1 time [milliseconds] Svar : 11 00 10 10. 11 1 0 -1 0 0.5 1 time [milliseconds] 10 1 0 -1 0 0.5 1 time [milliseconds] Exempel 1: Till höger visas fyra symboler som används av ett s.k. 4PSK-modem (PSK=Phase Shift Keying). De fyra symbolerna representerar bitföljderna 00, 01, 11 resp 10. a) Nedan visas utsignalen från det sändande modemet. Vilket meddelande, dvs vilken bitsekvens, överförs? b) Tidsaxeln är graderad i tusendels sekunder. Vad är symbolhastigheten i baud eller symboler/sekund? c) Vad är bithastigheten i bit per sekund (bps)? Svar: 1/1ms = 1000 symber per sekund = 1kbaud. Svar: 2000bps.

  22. Exempel 2: Nedan visas åtta symboler som används av ett s.k. 8QAM-modem (QAM=Quadrature Amplitude Modulation). Symbolerna i övre raden representerar bitföljderna 000, 001, 011 resp 010 (från vänster till höger). Undre raden representerar 100, 101, 111 resp 110.

  23. Forts exempel 2:

  24. Example 1 An analog signal carries 4 bits in each signal unit. If 1000 signal units are sent per second, find the baud rate and the bit rate Solution Baud rate = 1000 bauds per second (baud/s) Bit rate = 1000 x 4 = 4000 bps

  25. Figure 5.4Relationship between baud rate and bandwidth in ASK

  26. Figure 5.3ASK

  27. Example 3 Find the minimum bandwidth for an ASK signal transmitting at 2000 bps. The transmission mode is half-duplex. Solution In ASK the baud rate and bit rate are the same. The baud rate is therefore 2000. An ASK signal requires a minimum bandwidth equal to its baud rate. Therefore, the minimum bandwidth is 2000 Hz.

  28. Example 4 Given a bandwidth of 5000 Hz for an ASK signal, what are the baud rate and bit rate? Solution In ASK the baud rate is the same as the bandwidth, which means the baud rate is 5000. But because the baud rate and the bit rate are also the same for ASK, the bit rate is 5000 bps.

  29. Example 6 Find the minimum bandwidth for an FSK signal transmitting at 2000 bps. Transmission is in half-duplex mode, and the carriers are separated by 3000 Hz. Solution For FSK BW = baud rate + fc1- fc0 BW = bit rate + fc1 - fc0 = 2000 + 3000 = 5000 Hz

  30. Example 7 Find the maximum bit rates for an FSK signal if the bandwidth of the medium is 12,000 Hz and the difference between the two carriers is 2000 Hz. Transmission is in full-duplex mode. Solution Because the transmission is full duplex, only 6000 Hz is allocated for each direction. BW = baud rate + fc1 - fc0 Baud rate = BW - (fc1 - fc0 ) = 6000 - 2000 = 4000 But because the baud rate is the same as the bit rate, the bit rate is 4000 bps.

  31. Figure 5.8PSK

  32. Figure 5.5Solution to Example 5

  33. Figure 5.6FSK

  34. Figure 5.9PSK constellation

  35. Figure 5.10The 4-PSK method

  36. Figure 5.11The 4-PSK characteristics

  37. Figure 5.12The 8-PSK characteristics

  38. Figure 5.13Relationship between baud rate and bandwidth in PSK

  39. Example 9 Given a bandwidth of 5000 Hz for an 8-PSK signal, what are the baud rate and bit rate? Solution For PSK the baud rate is the same as the bandwidth, which means the baud rate is 5000. But in 8-PSK the bit rate is 3 times the baud rate, so the bit rate is 15,000 bps.

  40. Note: Quadrature amplitude modulation is a combination of ASK and PSK so that a maximum contrast between each signal unit (bit, dibit, tribit, and so on) is achieved.

  41. Figure 5.14The 4-QAM and 8-QAM constellations

  42. Figure 5.15Time domain for an 8-QAM signal

  43. Figure 5.1616-QAM constellations

  44. Figure 5.17Bit and baud

  45. Table 5.1 Bit and baud rate comparison

  46. Example 10 A constellation diagram consists of eight equally spaced points on a circle. If the bit rate is 4800 bps, what is the baud rate? Solution The constellation indicates 8-PSK with the points 45 degrees apart. Since 23 = 8, 3 bits are transmitted with each signal unit. Therefore, the baud rate is 4800 / 3 = 1600 baud

  47. Example 11 Compute the bit rate for a 1000-baud 16-QAM signal. Solution A 16-QAM signal has 4 bits per signal unit since log216 = 4. Thus, 1000·4 = 4000 bps

  48. Example 12 Compute the baud rate for a 72,000-bps 64-QAM signal. Solution A 64-QAM signal has 6 bits per signal unit since log2 64 = 6. Thus, 72000 / 6 = 12,000 baud

  49. 5.2 Telephone Modems Modem Standards

  50. Note: A telephone line has a bandwidth of almost 2400 Hz for data transmission.

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