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KLKSK. Pertemuan III Analog & Digital Data Shannon Theorem xDSL. Analog and Digital Signaling of Analog and Digital Data. Analog signals: represents data with continuously varying electromagnetic wave Digital signals: represents data with sequence of voltage pulses. Data and Signals.

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  1. KLKSK Pertemuan III Analog & Digital Data Shannon Theorem xDSL

  2. Analog and Digital Signaling of Analog and Digital Data • Analog signals: represents data with continuously varying electromagnetic wave • Digital signals: represents data with sequence of voltage pulses

  3. Data and Signals • Usually use digital signals for digital data and analog signals for analog data • Can use analog signal to carry digital data • Modem • Can use digital signal to carry analog data • Compact Disc audio

  4. Analog & Digital Transmission Data and Signal

  5. Analog Signals Carrying Analog and Digital Data

  6. Digital Signals Carrying Analog and Digital Data

  7. Analog & Digital Transmission Treatment of Signals

  8. Channel Capacity • Data rate • In bits per second • Rate at which data can be communicated • Bandwidth • In cycles per second of Hertz • Constrained by transmitter and medium

  9. Nyquist Bandwidth • If rate of signal transmission is 2B then signal with frequencies no greater than B is sufficient to carry signal rate • Given bandwidth B, highest signal rate is 2B • Given binary signal, data rate supported by B Hz is 2B bps • Can be increased by using M signal levels • C= 2B log2M • M is the of discrete signal or voltage levels

  10. Shannon Capacity Formula • Consider data rate, noise and error rate • Faster data rate shortens each bit so burst of noise affects more bits • At given noise level, high data rate means higher error rate • Signal to noise ratio (in decibels) • SNRdb=10 log10 (signal/noise) • Capacity C=B log2(1+SNR)

  11. Consider a voice channel being used, via modem, to transmit digital data. Assume a bandwidth of 3100 Hz. A typical value of S/N for a voice-grade line is 30 dB; or a ratio of 1000:1 • Thus • C = 3100 log2(1 + 1000) = 30,894 bps

  12. Shannon proved that if the actual information rate on a channel is less than the error-free capacity, then it is theoretically possible to use a suitable signal code to achieve error – free transmission through the channel • Unfortunately Shannon formula does not suggest a means for finding such codes

  13. Eb/No : ratio of signal energy per bit to noise power density per hertz • Consider a signal, digital or analog, that contains binary digital data transmitted at a certain bit rate R • 1 W = 1 J/s • The energy per bit in a signal Eb = STb • S : the signal power • Tb : the time required to send one bit • The data rate R = 1/Tb • (Eb/No) = (S/R)/No = S/(kTR) • Eb/No = S – 10log R + 228.6 dBW – 10 logT

  14. Ex. For binary phase-shift keying, Eb/No = 8.4 dB is required for a bit error rate of 10-4 (probability of error = 10-4). If the effective noise temperature is 290oK (room temperature) and the data rate is 2400 bps, what received signal level is required?

  15. Ans. • 8.4 = S (dBW) – 10 log 2400 + 228.6 dBW – 10 log 290 • = S (dBW) – (10) (3.38) + 228.6 – (10)(2.46) • S = -161.8 dBW

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