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CS 313 Introduction to Computer Networking & Telecommunication Theoretical Basis of Data Communication Chi-Cheng Lin, Winona State University Topics Data Communication Performance Measurements Analog/Digital Signals Time and Frequency Domains Bandwidth and Channel Capacity 2 Data Communication Performance Measurements Throughput How fast data can pass through an entity Number of bits passing through an imaginary wall in a second Bit time Duration of a bit (time for a bit ejected into network) 1 / throughput Propagation time (propagation delay) Time required for one bit to travel from one point to another Propagation speed depends on medium and signal frequency 3 Message Transmission Delay Total transmission delay = (size_of_message / throughput) + propagation_time Sender 01101… Time 01101… Receiver t0 t1 first bit last bit sent sent t2 t3 first bit last bit arrived arrived propagation_time 4 Message Transmission Delay - Example What is the transmission delay of a 2 KB message transmitted over a 2 km cable that has a throughput 40 Mbps and a propagation delay of 8 µs/km? Answer: Total transmission delay = (size_of_message / throughput) + propagation_time = (2048 x 8 bits / 40x106 bits/sec) + 8 µs/km x 2 km = 409.6 x 10-6 sec + 16 µs = 425.6 µs What is the bit time? 5 Signals Information must be transformed into electromagnetic signals to be transmitted Signal forms Analog or digital 6 Analog/Digital Signals Analog signal Continuous waveform Can have a infinite number of values in a range Digital signal Discrete Can have only a limited number of values E.g., 0 and 1, i.e., two levels, for binary signal 7 Time Vs. Frequency Domain A signal can be represented in either the time domain or the frequency domain. 8 Period (Time) and Frequency Unit Seconds (s) Equivalent 1s Unit Hertz (Hz) Equivalent 1 Hz Milliseconds (ms) 10–3 s Kilohertz (KHz) 103 Hz Microseconds (ms) 10–6 s Megahertz (MHz) 106 Hz Nanoseconds (ns) 10–9 s Gigahertz (GHz) 109 Hz Picoseconds (ps) 10–12 s Terahertz (THz) 1012 Hz 9 Composite Signals A composite signal can be decomposed into component sine waves - harmonics The decomposition is performed by Fourier Analysis DC component is the one with frequency 0. 10 Frequency Spectrum and Bandwidth Frequency spectrum Collection of all component frequencies it contains Bandwidth Width of frequency spectrum 11 Digital Signal - Decomposition A digital signal can be decomposed into an infinite number of simple sine waves (harmonics) A digital signal is a composite signal with an infinite bandwidth. More harmonics components = better approximation Animation Significant spectrum Components required to reconstruct the digital signal 12 Bandwidth-Limited Signals (a) A binary signal and its root-meansquare Fourier amplitudes. 13 Bandwidth-Limited Signals (2) (b) – (e) Successive approximations to the original signal. 14 Channel Capacity Channel capacity Maximum bit rate a transmission medium can transfer Nyquist theorem for noiseless channels C = 2H log2V where C: channel capacity (bit per second) H: bandwidth (Hz) V: signal levels (2 for binary) C is proportional to H bandwidth puts a limit on channel capacity 15 Channel Capacity Shannon Capacity for noisy channels C = H log2(1 + S/N) where C: (noisy) channel capacity (bps) H: bandwidth (Hz) S/N: signal-to-noise ratio dB = 10 log10 S/N In practice, we have to apply both for determining the channel capacity. 16 Examples Noiseless channel. Consider a noiseless channel with a bandwidth of 3000 Hz transmitting a signal with two signal levels. What is the maximum bit rate of this channel? Noiseless channel. Consider the same noiseless channel, transmitting a signal with four signal levels (for each level, we send two bits). What is the maximum bit rate of this channel? Extremely noisy channel. Consider an extremely noisy channel in which the value of the signal-to-noise ratio is almost zero. In other words, the noise is so strong that the signal is faint. What is the channel capacity of this channel? 17 Examples Theoretical highest bit rate of a regular telephone line. A telephone line normally has a bandwidth of 3000 Hz (300 Hz to 3300 Hz). The signal-to-noise ratio is usually 35dB, i.e., 3162. What is the capacity of this channel? Applying both theorems. We have a channel with a 2 MHz bandwidth. The S/N for this channel is 127; what is the appropriate bit rate and signal level? 18