Chapter 3 Data Transmission COSC 3213 Summer 2003 Courtesy of Prof. Amir Asif
Definitions 1. Recall that the lowest layer in OSI is the physical layer. The physical layer deals with the transfer of raw bits and is the focus of our attention in the chapters 3-6. 2. A transmission media can be classified in two categories: a. Guided media: directs signals along a physical path, e.g., twisted pair or coax. b. Unguided media that provides a means for transmission without guiding the signal, e.g., air, vacuum, and sea/ocean water. 3. Guided transmission can further be classified in two categories: a. Point-to-point where there is a direct link between two users who are the only devices sharing the medium. b. Multipoint where more than two devices share a network. 4. Based on the type of connectivity, transmission is of different types: a. Simplex: where communication can take place in only one direction b. Half-Duplex: where communication can take place in both directions but one station transmits at one time. c. Duplex: where both transmitter and receiver can transmit simultaneously. 5. Data: information that needs to be transmitted, e.g. voice signal, binary file. Signals: means of transmitting data, e.g., sine wave or line codes 2
Definitions (2) 6. Communication systems can be classified in two categories: a. Analog Communication System typically deals with analog signals b. Digital Communication System typically deals with digital signals 7. Analog signals are defined for the entire duration and can have any value. 8. Discrete-time signals are defined at particular instants but can have any value. 9. Digital signals are defined at fixed instants and can only have one of the pre-selected set of values. Analog Signal: Defined for all time Can have any amplitude Discrete-time Signal: Defined for multiples of T Can have any amplitude Digital Signal: Defined for multiples of T Amplitude limited to a few levels 3
Periodic Signals 1. Periodic signals repeats over time, i.e., s ( t) = s( t + T ) for all T 2. Aperiodic signals do not repeat themselves regularly. 4
Periodic Signals: Example 5
Periodic Signals: Properties 1. A periodic signal is completely specified through the following parameters: a. Peak Amplitude (A): Maximum value of the signal b. Fundamental frequency (f): Rate at which the signal repeats itself c. Phase (φ): Measure of relative position of the signal in time. 2. Other parameters that can be obtained from (a) (c). a. Period (T): Amount of time in it takes for the signal to repeat itself, T = 1/f b. Wavelength (λ): Distance in meters between two points of corresponding phase between two consecutive cycles. ct λ = or c 3. Any periodic signal with a fundamental frequency can be expressed as a linear combination of sinusoidal signals with fundamental frequencies that are integer multiple of the fundamental frequency (Fourier Series). f o f f o 6
Periodic Signals: Sine wave Identify the amplitude, fundamental frequency, and phase of the sinusoidal signals? 7
Periodic Signals: Fourier Series Expansion Recall property (3) in slide 8: Any periodic signal with a fundamental frequency can be expressed as a linear combination of sinusoidal signals with fundamental frequencies that are integer multiple of the fundamental frequency (Fourier Series). f o Ao x( t) = + 2 n= 1 where T 2 Ao = x( t) dt T 0 T 2 An = x( t)cos T 0 T 2 Bn = x( t)sin T 0 Example: Calculate the Fourier Series coefficients of a square wave with period T? f o [ A cos( 2πnf t) + B sin( 2πnf t) ] n ( 2πnf t) o ( 2πnf t) o dt dt o [ cos( 2πf t) (1/ 3) cos( 2π(3 f ) t) + (1/ 5) cos( 2π(5 f ) t) (1/ 7) cos( 2π(7 f ) ) +] x( t) = (4 A / π) 1 1 1 1 t n o 8
Periodic Signals First two terms of Fourier Series of a Sinusoidal Signal 9
Periodic Signals: Fourier Series Expressions 10
Aperiodic Signals 1. Aperiodic Signals do not repeat themselves 2. It is possible to derive Fourier representations of aperiodic signals using Fourier transform. j2πft X ( f ) = x( t) e dt 3. Expressions for Fourier transform of common aperiodic signals are given in Figure 3.16 of the text. 11
Frequency Representation 1. Any signal (periodic or aperiodic) can be represented either in time domain or in the frequency domain. 2. Frequency Spectrum: is the plot illustrating the range of frequencies present in a signal. 3. Absolute Bandwidth: is the width of the spectrum, or, the difference between the maximum and minimum frequency in the signal. 4. Most time-constrained signals have infinite theoretical bandwidth. We define effective bandwidth as the range of frequencies where most of the energy of the signals lie. 12
Relationship between Data Rate and Bandwidth 13
Frequency Representation: Audio Speech 100 Hz to 7kHz Spectrum Chosen: 300 to 3400 Hz Bandwidth: 3100 Hz Music: Bandwidth: 11kHz NTSC Video: Bandwidth: 4MHz 14
Analog Signaling Recall the difference between signals and data: Data: Information that needs to be transmitted Signal: waveform used to transmit data Both analog and digital data can be represented by analog signals 15
Analog Signaling: Digital Modulation (1) Amplitude Shift Keying (ASK): Represent bit 1 with sin(2πf c t) Represent bit 0 with 0 Volts Information 1 0 1 1 0 1 ASK 0 T 2T 3T 4T 5T 6T t 16
Analog Signaling: Digital Modulation (2) Frequency Shift Keying (FSK): Represent bit 1 with sin(2πf 1 t) Represent bit 0 with sin(2πf 2 t) Information 1 0 1 1 0 1 ASK 0 T 2T 3T 4T 5T 6T t FSK 0 T 2T 3T 4T 5T 6T t 17
Analog Signaling: Digital Modulation (3) Phase Shift Keying (PSK): Represent bit 1 with sin(2πf c t) Represent bit 0 with sin(2πf c t + π) = sin(2πf c t) Information 1 0 1 1 0 1 ASK 0 T 2T 3T 4T 5T 6T t FSK 0 T 2T 3T 4T 5T 6T t PSK 0 T 2T 3T 4T 5T 6T t 18
Digital Signaling Both analog and digital data can also be represented by digital signals 19
Analog to Digital Conversion (1) There are two steps involved in converting an analog signal to a digital signal: 1. Sampling: obtain the value of signal every T seconds. Choice of T is determined by how fast a signal changes, i.e., the frequency content of the signal Nyquist Sampling theorem says: Sampling rate (1/ T) 2 x maximum frequency in the signal T 5 /2 /2 /2 5 /2 Sampling 5 /2 /2 /2 5 /2 Analog Signal: Defined for all time Can have any amplitude Discrete-time Signal: Defined for multiples of T Can have any amplitude 20
Anologue to Digital Conversion (2) There are two steps involved in converting an analog signal to a digital signal: 2. Quantization: approximate signal to certain levels. Number of levels used determine the resolution. T T 5 /2 /2 /2 5 /2 Quantization 5 /2 /2 /2 5 /2 Discrete-time Signal: Defined for multiples of T Can have any amplitude Digital Signal: Defined for multiples of T Amplitude limited to a few levels Question: What is the minimum transmission rate needed for a signal quantized to L levels and sampled with a sampling rate of 1/T samples/second? Answer: 1 / T log 2 (L) 21
Digital Signal: Text 22
Transmission Recall the difference between analog and digital transmission / communication a. Analog Communication System typically deals with analog signals b. Digital Communication System typically deals with digital signals Analog Signal Digital Signal Analog Transmission Amplifiers used over long distances Not used Digital Transmission Analog signal represents digital data. Signal is propagated through repeaters. At each repeater, digital data is recovered. Digital signal (0 or 1) represents analog or digital data. Signal is propagated through repeaters. At each repeater, stream of 0s and 1s is recovered. 23
Analog vs Digital Transmission Digital transmission is preferable due to the following reasons 1. Low cost of digital technology such as VLSI technology with higher production. 2. Data integrity (or recovery) with the use of repeaters, where digital data is reproduced to eliminate the effects of cumulative noise. 3. Encryption techniques for digital data allows security and privacy. 4. Integration of digital and analog data into digital signals allows them to be treated similarly without any change in the transmission system. 5. Multiplexing of digital data allows higher utilization of the channel capacity. 24
Why Digital Communications (1)? Digital Communications results in an improved Signal to Noise ratio (SNR) as compared to analogue communications. Signal Tx Signal Rx Transmitter Analogue Channel Introduces distortion Receiver Equalized Signal Equalizer Repeater Amp. Example of an Analogue Communication System: Signal is not recovered perfectly once a distortion is introduced. 25
Why Digital Communications (2)? Transmitter Digital Channel Introduces distortion Repeater Receiver Decision Circuit & Signal Regenerator Amplifier Equalizer Timing Recovery Example of a Digital Communication System: Signal is recovered perfectly even when a distortion is introduced. 26
Transmission Impairments Transmission impairments causes the received signal to be different from the transmitted signal. (The received signal suffers from distortion.) Distortion is the result of several phenomena including 1. Attenuation: Reduction in the strength of signal over longer distances. Not only is the signal attenuated but the attenuation is different over different frequencies present in the signal. 2. Delay Distortion: Velocity of the signal propagation is different for different frequencies present in the signal. Various frequency components arrive at the receiver at different times resulting in phase shifts at different frequencies. 3. Noise: added from crosstalk, intermodulation, impulse spikes, and heating of electronic components (thermal noise) Thermal noise is due to thermal agitation of electrons resulting in heating. Thermal noise in Watts resulting from an electronic component is given by N = ktb where T = k = Boltzman constant temperature in o = 1.3803 10 K, B= Bandwidth in Hz 23 J / o K Example: Calculate the thermal noise in db for an effective noise temperature of 100 o K and a 10 MHz bandwidth? 27
Channel capacity (1) 1. Bit rate: is the number of bits that can be transmitted per second. Bit rate is measured in bits per second (bps) or Bytes per second (Bps). 2. Bandwidth (B): provides a measure of the range of frequencies that can be transmitted through a channel. 3. Fundamental Question: How fast (maximum bit rate) and reliably (probability of error) digital transmission can occur through a channel? Depends upon a number of factor: Amount of energy present in the signal Noise properties of the channel Distance for signal to propagate Bandwidth (BW) of the transmission medium 4. Channel Capacity (C) is the maximum bit rate supported by a channel. Channel Capacity can be calculated from two criterion: a. Nyquist Limit (when the channel is free of noise) : C = 2B log 2 (M) where M is the number of discrete signal levels Example: Calculate the Nyquist limit for a channel with BW = 1KHz if 16 levels are allowable to represent the discrete signal. 28
Channel Capacity (2) Can C = 2B log 2 (M) be made infinite by increase M? No! There are other constraints like the Signal to Noise ratio (SNR). signal noise signal + noise High SNR t t t signal noise signal + noise Low SNR t t t 29
Channel Capacity (3) By increasing m, the difference between adjacent levels is reduced affecting SNR Reduction in SNR affects the Channel Capacity (C). Shannon Channel Capacity theorem provides an upper bound on the channel capacity in terms of BW C = W log 2 (1 + SNR) bps Example: Calculate the channel capacity of a dial-in modem that has a BW of 3400 Hz if the best SNR possible in the modem is 34 db. 30