Digital to Analog Many carrier facilities are analog Many transmission media are also analog (microwave, radio) We can carry digital values over analog signals We must ‘encode’ the digital data over the digital signal This is what is done with modems Modem digitalAnalog Modem = Modulation/Demodulation

Encoding Digital Data We can encode data (bits) onto regular analog sine waves or example. Consider a sine wave y = sin(x)

Analog Signal Beyond a basic period, the wave repeats itself The time for one non repeating part of the signal is called the period The number of times the wave repeats itself during a unit of time is called the frequency Units of measure are usually the number of cycles (repetitions) per second Cycles per second are called Hertz frequency = 1 / period

Analog Signal Each signal has an amplitude or level

Analog Signal Each Signal has a frequency

Analog Signal Signal can also have a phase shift

Encoding bits with Analog Signals Encoding using amplitude change

Encoding by changing frequency

Encoding by changing signal phase

Encoding bits with Analog Signals

Bandwidth Bandwidth is a measure of channel or circuit capacity Bandwidth is in part determined by the number of times a signal changes value or frequency Frequency is measured in Hertz Both digital and Analog signals have frequency Every circuit or channel has a frequency limit  Due to Hardware  Due to limitation of media  Artificially introduced Data bandwidth is the capacity of a circuit to carry data and is usually measure in bits per second or bps

Bandwidth Consider a regular home phone line  This is an analog circuit  The frequency of that signal is limited by the phone company  The circuit carries sound in frequencies between 300 Hz and 3300 Hz  For separation the phone company allocates 4000 Hz for each phone line or phone call

Baud Rate Speed of a circuit is measured in baud Baud  The number of times a circuit can change value  If each change represents 1 bit then Baud Rate = Bit Rate  In all our previous examples Baud Rate = Bit Rate

Suppose we could create a number of levels, for example, say we had 8 voltages levels we could use

Suppose we receive

Maximum Data Rate of a Channel ** Harry Nyquist (1924) showed Max data rate (bps) = 2 * H * log2(V) Where H = frequency of channel in Hertz V = number of distinct signal levels Example – Voice grade line Hz (3000 usable) If we use 2 signal levels MDR = 2 * 3000 * log2(2) = 6,000 bps

Nyquist’s Result This result assumes a noiseless channel We never have a ‘clean’ channel  Noise  Distortion  Attenuation  Interference Circuits have a rating called Signal to Noise Ratio – measured in decibels S = measure of the power of the signal N = measure of the power of the noise

Limitations of Hardware Regardless of transmission type, signals degrade over distances  Level or power of signal may degrade, called attenuation  Shape of signal may degrade, especially digital signals. This is called distortion.  Interference from external sources (NEXT) So, how fast can we send bits? How short can we make a ‘bit time’? Maximum bit rate is therefore limited by the media and the sensitivity of hardware to be able to accurately recreate transmitted bits

Attenuation Signals on any media are subject loss of signal strength over distances Let P0 = initial power of a signal Pm = measured power at some distance of m unit Power ratio = Common measure is decibels ***

Maximum Data Rate for ‘noisy’ channel Signal to Noise ratio = S/N Decibel = 10 * log10(S/N) Claude Shannon (1948) Maximum data rate of a channel ** = H * log2( 1 + S/N) H = frequency of channel Example – voice grade line Signal to noise is approximately 30 DB Mdr = 3000 * log2( ) = 3000 * log2( 1001 ) = 30,000 (approximately) Regardless of the number of signals used

Modems Encode digital values over analog circuits To encode data, modems use combinations of  Amplitude Shift Keying (ASK)  Frequency Shift Keying (FSK)  Phase Shift Keying (PSK) Typically, a carrier frequency is provided and various SHIFT KEYING is applied For half duplex we could have only one carrier For full duplex, we need two carriers, one for each direction

Modems There have been many modem standards over time Early modems used a form of frequency shifting – Ex 300 bps full duplex modem  Originating modem Sine wave at 1070 Hz for a 0 bit Sine wave at 1270 Hz for a 1 bit  Answering modem Sine wave at 2025 Hz for a 0 bit Sine wave at 2225 Hz for a 1 bit

Modems Later modems used combinations of shift keying by combining PSK and ASK Some common 9600 bps modems used  12 phase shifts at 1 amplitude  4 phase shift at a second amplitude  Combination of 16 different states  Called Quadrature Amplitude Modulation (QAM)  Baud rate was 2400 cycles per second  Each of the 16 states represented 4 bits

Modem Constellation

Modems Standard BaudBit Modulation raterate Technique V FSK V /1200 PSK V.22bis /2400 QAM V FSK V /9600 QAM/TCM V ,800 V ,000 V ,000

Modems To improve performance, compression and error correction standards developed Two compression standards in in vogue  V.42bis  MNP 5 Two error correction standards  V.42  MNP 4