basics of data transmission

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

2. 1-2

3. 1-3 Periodic vs. Aperiodic Signals Periodic signal Pattern repeated over time s(t+T) = s(t) Aperiodic signal Pattern not repeated over time

4. 1-4 Sine Wave 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

5. 1-5 Signals in Frequency Domain Signal is made up of many components Components are sine waves 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

6. 1-6 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(2pft)

7. 1-7 Time and Frequency Domains: Example 2

8. 1-8 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(2pft) + sin(2p3ft)] A: 2f Hz

9. 1-9 Frequency Domain (cont�d) Q. What is the absolute bandwidth of square wave?

10. 1-10 Approximation of Square Wave

11. 1-11 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. 1-12 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 two bits 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. 1-13 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. 1-14 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. 1-15 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. 1-16 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. 1-17 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. 1-18 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. 1-19 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. 1-20 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. 1-21 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. 1-22 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. 1-23 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. 1-24 Analog Signals Carrying Analog and Digital Data

25. 1-25 Digital Signals Carrying Analog and Digital Data

26. 1-26 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. 1-27 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. 1-28 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. 1-29 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