Chi-Cheng Lin, Winona State University CS 313 Introduction to Computer Networking & Telecommunication Theoretical Basis of Data Communication

2 Topics l Data Communication Performance Measurements l Analog/Digital Signals l Time and Frequency Domains l Bandwidth and Channel Capacity

3 Data Communication Performance Measurements l Throughput  How fast data can pass through an entity  Number of bits passing through an imaginary wall in a second l Bit time  Duration of a bit (time for a bit ejected into network)  1 / throughput l Propagation time (propagation delay)  Time required for one bit to travel from one point to another  Propagation speed depends on medium and signal frequency

4 Message Transmission Delay Total transmission delay = (size_of_message / throughput) + propagation_time Sender Receiver t0t0 t1t1 t2t2 t3t3 first bit sent last bit sent first bit arrived last bit arrived Time propagation_time 01101…

5 Message Transmission Delay - Example l 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? l Answer: Total transmission delay = (size_of_message / throughput) + propagation_time = (2048 x 8 bits / 40x10 6 bits/sec) + 8 µs/km x 2 km = x sec + 16 µs = µs What is the bit time?

6 Signals l Information must be transformed into electromagnetic signals to be transmitted l Signal forms  Analog or digital

7 Analog/Digital Signals l Analog signal  Continuous waveform  Can have a infinite number of values in a range l Digital signal  Discrete  Can have only a limited number of values  E.g., 0 and 1, i.e., two levels, for binary signal

8 Time Vs. Frequency Domain l A signal can be represented in either the time domain or the frequency domain.

9 UnitEquivalentUnitEquivalent Seconds (s)1 sHertz (Hz)1 Hz Milliseconds (ms)10 –3 sKilohertz (KHz)10 3 Hz Microseconds (ms)10 –6 sMegahertz (MHz)10 6 Hz Nanoseconds (ns)10 –9 sGigahertz (GHz)10 9 Hz Picoseconds (ps)10 –12 sTerahertz (THz)10 12 Hz Period (Time) and Frequency

10 Composite Signals l A composite signal can be decomposed into component sine waves - harmonics l The decomposition is performed by Fourier Analysis l DC component is the one with frequency 0.

11 Frequency Spectrum and Bandwidth l Frequency spectrum  Collection of all component frequencies it contains l Bandwidth  Width of frequency spectrum

12 Digital Signal - Decomposition l 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.  A digital signal is a composite signal with an infinite bandwidth. l More harmonics components = better approximation  AnimationAnimation l Significant spectrum  Components required to reconstruct the digital signal

13 Bandwidth-Limited Signals l (a) A binary signal and its root-mean- square Fourier amplitudes.

14 Bandwidth-Limited Signals (2) l (b) – (e) Successive approximations to the original signal.

15 Channel Capacity l Channel capacity  Maximum bit rate a transmission medium can transfer l Nyquist theorem for noiseless channels  C = 2H log 2 V 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

16 Channel Capacity l Shannon Capacity for noisy channels  C = H log 2 (1 + S/N) where C: (noisy) channel capacity (bps) H: bandwidth (Hz) S/N: signal-to-noise ratio dB = 10 log 10 S/N l In practice, we have to apply both for determining the channel capacity.

17 Examples l 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? l 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? l 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?

18 Examples l 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., What is the capacity of this channel? l 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?