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Basics of Data Transmission

Basics of Data Transmission. Our Objective is to understand … Signals, bandwidth, data rate concepts Transmission impairments Channel capacity Data Transmission. A signal is generated by a transmitter and transmitted over a medium function of time

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Basics of Data Transmission

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  1. Basics of Data Transmission Our Objective is to understand … • Signals, bandwidth, data rate concepts • Transmission impairments • Channel capacity • Data Transmission

  2. A signal is generated by a transmitter and transmitted over a medium function of time function of frequency, i.e., composed of components of different frequencies Analog signal varies smoothly with time E.g., speech Digital signal maintains a constant level for some period of time, then changes to another level E.g., binary 1s and 0s Signals

  3. Periodic signal Pattern repeated over time s(t+T) = s(t) Aperiodic signal Pattern not repeated over time Periodic vs. Aperiodic Signals

  4. The fundamental periodic signal 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 Sine Wave

  5. Signals in Frequency Domain • Signal is made up of many components • Components are sinewaves with different frequencies • In early 19th century, Fourier proved that • Any periodic function can be constructed as the sum of a (possibly infinite) number of sines and cosines • This decomposition is called Fourier series • f is called the fundamental frequency • an, bn are amplitude of nthharmonic • c is a constant

  6. S(f) 1 f Frequency, f Frequency Domain (cont’d) • Fourier Theorem enables us to represent signal in Frequency Domain • i.e., to show constituent frequencies and amplitude of signal at these frequencies • Example 1: sine wave: s(t) = sin(2πft)

  7. Time and Frequency Domains: Example 2 Time domain s(t) Frequencydomain S(f)

  8. Frequency Domain (cont’d) • So, we can use Fourier theorem to represent a signal as function of its constituent frequencies, • and we know the amplitude of each constituent frequency. So what? • We know the spectrum of a signal, which is the range of frequencies it contains, and • Absolute bandwidth= width of the spectrum • Q: What is the bandwidth of the signal in the previous example? [sin(2πft) + sin(2π3ft)] • A: 2f Hz

  9. Frequency Domain (cont’d) • Q. What is the absolute bandwidth of square wave? • Hint: Fourier tells you that • Absolute BW = ∞ (ooops!!) • But, most of the energy is contained within a narrow band (why?) we refer to this band as effective bandwidth, or just bandwidth

  10. Approximation of Square Wave Using the first 3 harmonics, k=1, 3, 5 A. BW = 4*f Hz Using the first 4 harmonics, k=1, 3, 5, 7 A. BW = 6*f Hz Q. What is BW in each case? Cool applet on Fourier Series

  11. Signals and Channels • Signal • can be decomposed to components (frequencies) • spectrum: range of frequencies contained in signal • (effective) bandwidth: band of frequencies containing most of the energy • Communications channel (link) • has finite bandwidth determined by the physical properties (e.g., thickness of the wire) • truncates (or filters out) frequencies higher than its BW • i.e., it may distort signals • can carry signals with bandwidth ≤ channel bandwidth

  12. Bandwidth and Data Rate • Data rate: number of bits per second (bps) • Bandwidth: signal rate of change, cycles per sec (Hz) • Well, are they related? • Ex.: Consider square wave with high = 1 and low = 0  • We can send twobits every cycle (i.e., during T = 1/f sec) • Assume f =1 MHz (fundamental frequency)  T = 1 usec • Now, if we use the first approximation (3 harmonics) • BW of signal = (5 f – 1 f) = 4 f = 4 MHz • Data rate = 2 / T = 2 Mbps • So we need a channel with bandwidth 4 MHz to send at date rate 2 Mbps

  13. Bandwidth and Data Rate (cont’d) • But, if we use the second approx. (4 harmonics) • BW of signal = (7 f – 1 f) = 6 f = 6 MHz • Data rate = 2 / T = 2 Mbps • Which one to choose? Can we use only 2 harmonics (BW = 2 MHz)? • It depends on the ability of the receiver to discern the difference between 0 and 1 • Tradeoff: cost of medium vs. distortion of signal and complexity of receiver

  14. Bandwidth and Data Rate (cont’d) • Now, let us agree that the first appox. (3 harmonics) is good enough • Data rate of 2 Mbps requires BW of 4 MHz • To achieve 4 Mbps, what is the required BW? • data rate = 2 (bits) / T (period) = 4 Mbps  T = 1 /2 usec •  f (fundamental freq) = 1 /T = 2 MHz  • BW = 4 f = 8 MHz • Bottom line: there is a direct relationship between data rate and bandwidth • Higher data rates require more bandwidth • More bandwidth allows higher data rates to be sent

  15. Bandwidth and Data Rate (cont’d) • Nyquist Theorem: (Assume noise-free channel) • If rate of signal transmission is 2B then signal with frequencies no greater than B is sufficient to carry signal rate, OR alternatively • Given bandwidth B, highest signal rate is 2B • For binary signals • Two levels  we can send one bit (0 or 1) during each period  data rate (C) = 1 x signal rate = 2 B • That is, data rate supported by B Hz is 2B bps • For M-level signals • M levels  we can send log2M bits during each period  • C= 2B log2M

  16. Bandwidth and Data Rate (cont’d) • Shannon Capacity: • Considers data rate, (thermal) 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 • SNR ≡ Signal to noise ration • SNR = signal power / noise power • Usually given in decibels (dB): SNRdB=10 log10 (SNR) • Shannon proved that: C = B log2(1 + SNR) • This is theoretical capacity, in practice capacity is much lower (due to other types of noise)

  17. Bandwidth and Data Rate (cont’d) • Ex.: A channel has B = 1 MHz and SNRdB = 24 dB, what is the channel capacity limit? • SNRdB = 10 log10 (SNR)  SNR = 251 • C = B log2(1 + SNR) = 8 Mbps • Assume we can achieve the theatrical C, how many signal levels are required? • C = 2 B log2M  M = 16 levels

  18. Transmission Impairments • Signal received may differ from signal transmitted • Analog - degradation of signal quality • Digital - bit errors • Caused by • Attenuation and attenuation distortion • Delay distortion • Noise

  19. Attenuation • Signal strength falls off with distance • Depends on medium • Received signal strength: • must be enough to be detected • must be sufficiently higher than noise to be received without error • Attenuation is an increasing function of frequency  attenuation distortion

  20. Delay Distortion • Only in guided media • Propagation velocity varies with frequency • Critical for digital data • A sequence of bits is being transmitted • Delay distortion can cause some of signal components of one bit to spill over into other bit positions  • intersymbol interference, which is the major limitation to max bit rate

  21. Noise (1) • Additional signals inserted between transmitter and receiver • Thermal • Due to thermal agitation of electrons • Uniformly distributed across frequencies  • White noise • Intermodulation • Signals that are the sum and difference of original frequencies sharing a medium

  22. Noise (2) • Crosstalk • A signal from one line is picked up by another • Impulse • Irregular pulses or spikes, e.g. external electromagnetic interference • Short duration • High amplitude

  23. Data and Signals • Data • Entities that convey meaning • Analog: speech • Digital: text (character strings) • Signals • electromagnetic representations of data • Analog: continuous • Digital: discrete (pulses) • Transmission • Communication of data by propagation and processing of signals

  24. Analog Signals Carrying Analog and Digital Data

  25. Digital Signals Carrying Analog and Digital Data

  26. Analog Transmission • Analog signal transmitted without regard to content • May be analog or digital data • Attenuated over distance • Use amplifiers to boost signal • But, it also amplifies noise!

  27. Digital Transmission • Concerned with content • Integrity endangered by noise, attenuation • Repeaters used • Repeater receives signal • Extracts bit pattern • Retransmits • Attenuation is overcome • Noise is not amplified

  28. Advantages of Digital Transmission • Digital technology • Low cost LSI/VLSI technology • Data integrity • Longer distances over lower quality lines • Capacity utilization • High bandwidth links economical • High degree of multiplexing easier with digital techniques • Security & Privacy • Encryption • Integration • Can treat analog and digital data similarly

  29. Summary • Signal: composed of components (Fourier Series) • Spectrum, bandwidth, data rate • Shannon channel capacity • Transmission impairments • Attenuation, delay distortion, noise • Data vs. signals • Digital vs. Analog Transmission

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