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Data and Computer Communications Chapter 3 Data Transmission Required Reading: Stallings chapter 3 1 Physical Layer Source node Destination node Application Application Presentation Presentation Session Session transport Intermediate node transport Packets Network Network Network Frames Data link Data link Data link Physical Bits Physical Physical Signals 2 Physical / Data Link Layer Interface Sender Receiver NL HDR DLL Frame ACK PL HDR Transmitted Bits 3 Physical Layer Communications and Information Theory are topics of whole courses We‟ll cover some theoretical basics regarding communications over a physical channel We discover that there are physical limitations to communications over a given channel We‟ll cover some fundamental theorems 4 Terminology (1) Transmitter Receiver Medium Guided medium e.g. twisted pair, optical fiber Unguided medium e.g. air, water, vacuum 5 Terminology (2) Direct link No intermediate devices Point-to-point Direct link Only 2 devices share link Multi-point More than two devices share the link 6 Terminology (3) Simplex One direction (but in Europe means half duplex) e.g. Television Half duplex Either direction, but only one way at a time e.g. police radio Full duplex Both directions at the same time e.g. telephone 7 Electromagnetic Signals Function of time Analog (varies smoothly over time) Digital (constant level over time, followed by a change to another level) Function of frequency Spectrum (range of frequencies) Bandwidth (width of the spectrum) 8 Frequency, Spectrum and Bandwidth Time domain concepts Continuous signal Varies in a smooth way over time Discrete signal Maintains a constant level then changes to another constant level Periodic signal Pattern repeated over time Aperiodic signal Pattern not repeated over time 9 Periodic Signal Characteristics Amplitude (A): signal value, measured in volts Frequency (f ): repetition rate, cycles per second or Hertz Period (T): amount of time it takes for one repetition, T=1/f Phase (Φ): relative position in time, measured in degrees or radians 10 Analog Signaling represented by sine waves amplitude (volts) 1 cycle phase difference time (sec) frequency (hertz) = cycles per second 11 Digital Signaling represented by square waves or pulses amplitude (volts) 1 cycle time (sec) frequency (hertz) = cycles per second 12 Continuous & Discrete Signals 13 Periodic Signals 14 Sine Wave 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 15 Varying Sine Waves Sin2πt 0.5Sin2πt Phase Shift in radians Sin4πt or Phase Shift in seconds 16 Wavelength () Distance occupied by one cycle Distance between two points of corresponding phase in two consecutive cycles Assuming signal velocity in space is equal to v = vT or f = v Here, V=c = 3*108 ms-1 (speed of light in free space) 17 Frequency Domain Concepts A Signal is usually made up of many frequencies Components are sine waves It Can be shown (Fourier analysis) that any signal is made up of component sine waves One can plot frequency domain functions instead of/in addition to time domain functions 18 Addition of Frequency Components (a) Sin(2πft) (b) (1/3)Sin(2π(3f)t) 19 (c) (4/π)[Sin(2πft)+(1/3)Sin(2π(3f)t)] Frequency Domain Note: For square waves, only odd harmonics exist (plus the fundamental component of course). Figure a is discrete because (a) Frequency domain function for s(t)=(4/π)[Sin(2πft)+(1/3)Sin(2π(3f)t)] the time domain function is periodic. Figure b is continuous because the time domain function is aperiodic. See Figure 3.16 Page 103. Note that s(f) is of the form 20 (b) Frequency domain function for a single square pulse s(t)=1 for -X/2<t<X/2 Communications Basics Represent a signal as a single-valued function of time, g(t), to model behavior of a signal (may be voltage, current or other change) Jean-Baptiste Fourier showed we can represent a periodic signal (given some conditions) as the sum of a possibly infinite number of sines and cosines Period = T S g(t) = (1/2)c + n=1 an sin(2pnft) + S bn cos(2pnft) n=1 f = 1/T is fundamental frequency a & b coefficients are the amplitude of the nth harmonic This is a Fourier Series 21 Original Time -> Harmonic spectrum As we add more harmonics the signal reproduces the original more closely 22 Signal Transmission No transmission facility can transmit signals without losing some power Usually this attenuation is frequency dependent so the signal becomes distorted Generally signal is completely attenuated above some max frequency (due to medium characteristics or intentional filtering) The signal is bandwidth limited 23 Signal Transmission Time T necessary to transmit a character depends on coding method and signalling speed Signaling speed = number of times per second the signal changes value and is measured in baud Note that baud rate is not necessarily the same as the bit rate By limiting the bandwidth of the signal we also limit the data rate even if a channel is perfect Overcome this by encoding schemes 24 Spectrum & Bandwidth Spectrum range of frequencies contained in signal Absolute bandwidth width of spectrum Effective bandwidth Often just bandwidth Narrow band of frequencies containing most of the energy DC Component Component of zero frequency 25 Signal with DC Component (a) s(t)=1+(4/π)[Sin(2πft)+(1/3)Sin(2π(3f)t)] 26 Data Rate and Bandwidth Any transmission system has a limited band of frequencies This limits the data rate that can be carried See Figure 3.8 Page 79 27 Bandwidth Width of the spectrum of frequencies that can be transmitted if spectrum=300 to 3400Hz, bandwidth=3100Hz Greater bandwidth leads to greater costs Limited bandwidth leads to distortion Analog measured in Hertz, digital measured in baud 28 BPS vs. Baud BPS=bits per second Baud=# of signal changes per second Each signal change can represent more than one bit, through variations on amplitude, frequency, and/or phase 29 Analog and Digital Data Transmission Data Entities that convey meaning Signals Electric or electromagnetic representations of data Transmission Communication of data by propagation and processing of signals 30 Data Analog Continuous values within some interval e.g. sound, video Digital Discrete values e.g. text, integers 31 Acoustic Spectrum (Analog) 32 Signals Means by which data are propagated Analog Continuously variable Various media wire, fiber optic, space Speech bandwidth 100Hz to 7kHz Telephone bandwidth 300Hz to 3400Hz Video bandwidth 4MHz Digital Use two DC components 33 Digital Text Signaling Transmission of electronic pulses representing the binary digits 1 and 0 How do we represent letters, numbers, characters in binary form? Earliest example: Morse code (dots and dashes) Most common current form: ASCII 34 ASCII Character Codes Use 8 bits of data (1 byte) to transmit one character 8 binary bits has 256 possible outcomes (0 to 255) Represents alphanumeric characters, as well as “special” characters 35 Digital Image Signaling Pixelization and binary representation Code: 00000000 00111100 01110110 01111110 01111000 01111110 00111100 00000000 36 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 37 Why Study Analog? Telephone system is primarily analog rather than digital (designed to carry voice signals) Low-cost, transmission medium (present almost at all places at all times If we can convert digital information (1s and 0s) to analog form (audible tone), it can be transmitted inexpensively 38 Voice Signals Easily converted from sound frequencies (measured in loudness/db) to electromagnetic frequencies, measured in voltage Human voice has frequency components ranging from 20Hz to 20kHz For practical purposes, the telephone system has a narrower bandwidth than human voice, from 300 to 3400Hz 39 Analog Signals Carrying Analog and Digital Data 40 Digital Signals Carrying Analog and Digital Data 41 Analog Transmission Analog signal transmitted without regard to content May be analog or digital data Attenuated over distance Use amplifiers to boost signal Also amplifies noise 42 Digital Transmission Concerned with content Integrity endangered by noise, attenuation etc. Repeaters used Repeater receives signal Extracts bit pattern Retransmits Attenuation is overcome Noise is not amplified 43 Advantages of Digital Transmission Digital technology Low cost LSI/VLSI technology Data integrity Longer distances over lower quality lines Capacity utilization Economical high bandwidth links High degree of multiplexing easier with digital techniques Security & Privacy Encryption Integration Can treat analog and digital data similarly 44 Transmission Media the physical path between transmitter and receiver design factors bandwidth attenuation: weakening of signal over distances interference number of receivers 45 Impairments and Capacity Impairments exist in all forms of data transmission Analog signal impairments result in random modifications that impair signal quality Digital signal impairments result in bit errors (1s and 0s transposed) 46 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 47 Transmission Impairments Attenuation loss of signal strength over distance Attenuation Distortion different losses at different frequencies Delay Distortion different speeds for different frequencies Noise 48 Attenuation P1 watts P2 watts transmitter receiver Attenuation 10 log10 (P1/P2) dB Amplification 10 log10 (P2/P1) dB 49 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 50 Delay Distortion Only in guided media Propagation velocity varies with frequency 51 Noise (1) Additional signals inserted between transmitter and receiver Types of Noise: Thermal Due to thermal excitement of electrons Uniformly distributed, cannot be eliminated White noise Intermodulation Signals that are the sum and difference of original frequencies sharing a medium 52 Noise (2) Crosstalk A signal from one line is picked up by another NEXT (near-end crosstalk ) interference in a wire at the transmitting end of a signal sent on a different wire FEXT (far-end crosstalk) interference in a wire at the receiving end of a signal sent on a different wire Impulse Irregular pulses or spikes e.g. External electromagnetic interference Short duration High amplitude Less predictable 53 Noise Effect distorts a transmitted signal attenuates a transmitted signal signal-to-noise ratio to quantify noise S/Ndb = 10 log S S= average signal power N N= noise power 54 Effect of noise Signal Noise Logic Threshold Signal+Noise Sampling times 0 1 1 1 1 0 0 0 0 1 Data Received 0 1 0 1 1 0 0 1 0 1 Original data Bit error 55 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 56 Maximum Data Rate In 1920s Nyquist (of the Nyquist Theorem) developed an equation for the maximum data rate of a noiseless channel For low pass filtered signal of bandwidth B Sampling at exactly 2B samples per sec allows reconstruction of the signal More samples are useless since the frequencies above B are filtered out C=Capacity=max data rate = 2B log2 M bits/sec for M discrete levels 57 Nyquist theorem “ In a perfectly noiseless channel, if f is the maxmimum frequency the medium can transmit, the receiver can completely reconstruct a signal by sampling it 2*f times per second” Nyquist, 1920 58 Nyquist formula B = bandwidth C= 2B log2 M M = number of discrete signal levels Theoretical capacity for Noiseless channel Example: Channel capacity calculation for voice bandwidth (~3100 Hz): M Max data rate (C) 2 6200 bps 4 12400 bps 8 18600 bps 16 24800 bps 59 Shannon’s Law In the „40s Shannon (of Shannon‟s Law) extended the equation to a channel subject to thermodynamic (thermal) noise Thermal noise measured by ratio of signal (S) power to noise (N) power (signal-to-noise ratio - S/N) But represented as: 10 log10 S/N These units are called decibels (dB) Now, for a channel with signal to noise of S/N Capacity=C=max bits/sec = B log2 (1 + S/N) Here, C=Theoretical Maximum capacity with noise Note: Only much lower rates are achieved since the equation assumes zero impulse noise and no attenuation and delay distortion. 60 Bit rate and Baud rate Bit rate number of bits that are transmitted in a second Baud rate number of line signal changes (variations) per second If a modem transmits 1 bit for every signal change bit rate = baud rate If a signal change represents 2 or more or n bits bit rate = baud rate *n 61