Data and Computer Communications Chapter 3 – Data Transmission

Analog and Digital Signals

Periodic Signals

Sine Wave peak amplitude (A) – maximum strength of signal – typically measured in volts frequency (f) – rate at which the signal repeats – Hertz (Hz) or cycles per second – period (T) is the amount of time for one repetition – T = 1/f phase (  ) – relative position in time within a single period of signal (periodic continuous signal)

Varying Sine Waves s(t) = A sin(2  ft +  )

Wavelength ( ) the wavelength of a signal is the distance occupied by a single cycle can also be stated as the distance between two points of corresponding phase of two consecutive cycles assuming signal velocity v, then the wavelength is related to the period as = vT = vT or equivalently f = v especially when v=c c = 3*10 8 ms (speed of light in free space)c = 3*10 8 ms (speed of light in free space)

Frequency Domain Concepts signals are made up of many frequencies components are sine waves Fourier analysis can show that any signal is made up of components at various frequencies, in which each component is a sinusoid The latter frequency is referred to as the fundamental frequency. Each multiple of the fundamental frequency is referred to as a harmonic frequency of the signal.

Addition of Frequency Components (T=1/f) Fig. (c) is sum of Fig. (a) & Fig. (b) = f +3f

Frequency Domain Representations frequency domain function of Fig 3.4c frequency domain function of single square pulse

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 energy dc component component of zero frequency

Signal with dc Component

Data Rate and Bandwidth any transmission system has a limited band of frequencies this limits the data rate that can be carried on the transmission medium square waves have infinite components and hence an infinite bandwidth most energy in first few components limiting bandwidth creates distortions There is a direct relationship between data rate and bandwidth

Acoustic Spectrum (Analog)

Advantages & Disadvantages of Digital Signals

Audio Signals frequency range of typical speech is 100Hz-7kHz easily converted into electromagnetic signals varying volume converted to varying voltage can limit frequency range for voice channel to Hz

Conversion of PC Input to Digital Signal

Analog Signals

Digital Signals

Analog and Digital Transmission Impairments

Transmission Impairments signal received may differ from signal transmitted causing: – analog - degradation of signal quality – digital - bit errors Most significant impairments are – Attenuation and attenuation distortion – Delay distortion – Noise

Attenuation Received signal strength must be: strong enough to be detected sufficiently higher than noise to be received without error Strength can be increased using amplifiers or repeaters. Equalize attenuation across the band of frequencies used by using loading coils or amplifiers.  signal strength falls off with distance over any transmission medium  varies with frequency

Attenuation Distortion

Delay Distortion occurs because propagation velocity of a signal through a guided medium varies with frequency various frequency components arrive at different times resulting in phase shifts between the frequencies particularly critical (more damage) for digital data since parts of one bit spill over into others causing intersymbol interference

Noise unwanted signals inserted between transmitter and receiver is the major limiting factor in communications system performance

Noise Categories Noise may be divided into four categories: 1)Thermal noise (white noise) 2)Intermodulation noise 3)Crosstalk 4)Impulse noise

Categories of Noise (1,2) Thermal noise due to thermal agitation of electrons uniformly distributed across bandwidths referred to as white noise Intermodulation noise produced by nonlinearities in the transmitter, receiver, and/or intervening transmission medium effect is to produce signals at a frequency that is the sum or difference of the two original frequencies

Thermal Noise The amount of thermal noise to be found in a bandwidth of 1 Hz in any device or conductor is: N 0 = k *T in (W/Hz) N 0 = noise power density in watts per 1 Hz of bandwidth k = Boltzmann's constant = 1.38 * 10 –23 J/K T = temperature, in kelvin (absolute temperature), where C = K – 273K = C + 273

Example 1 A room temperature is usually specified as T = 17˚C, or 290 K. At this temperature, the thermal noise power density is: N 0 (in W/Hz) = (1.38 * ) *290 = 4 *10 –21 W/Hz N 0 (in dBw) = 10 log (K*T) = –204 dBW The “dBW” is the decibel-watt. The above thermal noise (N 0 ) is assumed to be independent of frequency. Thus the thermal noise in watts present in a bandwidth of B Hz can be expressed as: N (in W) = k *T *B in watts (W) N (in dBW)= 10 log (k*T*B) = 10 log k + 10 log T + 10 log B

Example 2 Given a receiver with an effective noise temperature of 294 K and a 10 MHz bandwidth, the thermal noise in decibel watts at the receiver's output is: N dB = 10 log K + 10 log T + 10 log B = – log (294) + 10 log 10 7 = – =–133.9 dBW

Categories of Noise (3,4) Crosstalk: – a signal from one line is picked up by another – can occur by electrical coupling between nearby twisted pairs or when microwave antennas pick up unwanted signals Impulse Noise: – caused by external electromagnetic interferences – noncontinuous, consisting of irregular pulses or spikes – short duration and high amplitude – minor annoyance for analog signals but a major source of error in digital data

Channel Capacity Maximum rate at which data can be transmitted over a given communications channel under given conditions data rate in bits per second bandwidth in cycles per second or Hertz noise average noise level over path error rate rate of corrupted bits limitations due to physical properties main constraint on achieving efficiency is noise

Data Transmission Rate  The rate at which data (file, voice, image, video,…) are transmitted.  Measured in bits per second (bps) or bytes per second.  1 byte = 8 bits.  Data Rate (bps) = Data Size (bits) / Time (sec.)  Number of Packets = File Size / Packet Payload  1Kbps = 10 3 bps  1Mbps = 10 6 bps  1Gbps = 10 9 bps

Wavelength, frequency & Speed The signal’s wavelength λ is the width (distance) of each cycle of the signal that has v velocity (speed) in a time period T where: λ = v T T=1/f λ = v/f λ * f= v If the signal has the light speed c (v=c = 3 * 10 8 m/s ) λ = c/f f = λ /c

Units and values λ (m)= v (m/sec) * T (sec) (in time domain) λ (m)= v (m/sec) /f (Hz) (in frequency domain) λ (wavelength) units and transformation: 1 mm (millimeter) = 1*10 -3 m 1 µm (micrometer)= 1*10 -6 m T (Time) units and transformation: 1 msec (millisecond) = 1*10 -3 sec 1 µsec (microsecond)= 1*10 -6 sec

Nyquist Bandwidth In the case of a channel that is noise free : if rate of signal transmission is 2B then can carry signal with frequencies no greater than B – given bandwidth B, highest signal rate is 2B for binary signals, 2B bps needs bandwidth B Hz can increase rate by using M signal levels Nyquist Formula is: C = 2B log 2 M data rate can be increased by increasing signals – however this increases burden on receiver – noise & other impairments limit the value of M

Shannon Capacity Formula considering the relation of data rate, noise and error rate for noisy channels: – faster data rate shortens each bit so bursts of noise corrupts more bits – given noise level, higher rates mean higher errors Shannon developed formula relating these to signal to noise ratio (in decibels) SNR db = 10 log 10 (signal/noise) Shannon capacity: C = B log 2 (1+SNR ) – theoretical maximum capacity – get much lower rates in practice

Example 1 Suppose that the spectrum of a channel is between 3 MHz and 4 MHz and SNR dB = 24 dB. Then B= 4 MHz – 3 MHz = 1 MHz = 10 6 Hz SNR dB = 24 dB = 10 log 10 (SNR) SNR= 251 dBW Using Shannon's formula: C= 10 6  log 2 ( )  10 6  8 = 8 Mbps

Example 2 Based on Nyquist's formula, how many signaling levels are required? We have C = 2B log 2 M 8  10 6 = 2  (10 6 )  log 2 M 4= log 2 M M = 16

Summary transmission concepts and terminology – guided/unguided media frequency, spectrum and bandwidth analog vs. digital signals data rate and bandwidth relationship transmission impairments – attenuation/delay distortion/noise channel capacity – Nyquist/Shannon