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 Signals  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

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 19 th 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  a n, b n are amplitude of n th harmonic  c is a constant

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(2πft) Frequency, f S(f) 1 f

7. 1-7 Time and Frequency Domains: Example 2 Time domain s(t) Frequency domain S(f)

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(2πft) + sin(2π3ft)]  A: 2f Hz

9. 1-9 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. 1-10 A. BW = 6*f Hz Approximation of Square Wave Using the first 3 harmonics, k=1, 3, 5 Using the first 4 harmonics, k=1, 3, 5, 7 Q. What is BW in each case? A. BW = 4*f Hz Cool applet on Fourier Series

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 log 2 M bits during each period   C= 2B log 2 M

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): SNR dB = 10 log 10 (SNR)  Shannon proved that: C = B log 2 (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 SNR dB = 24 dB, what is the channel capacity limit?  SNR dB = 10 log 10 (SNR)  SNR = 251  C = B log 2 (1 + SNR) = 8 Mbps  Assume we can achieve the theatrical C, how many signal levels are required?  C = 2 B log 2 M  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