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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

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

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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

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Analog Signal Each signal has an amplitude or level

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Analog Signal Each Signal has a frequency

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Analog Signal Signal can also have a phase shift

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Encoding bits with Analog Signals Encoding using amplitude change

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Encoding by changing frequency

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Encoding by changing signal phase

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Encoding bits with Analog Signals

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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

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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

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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

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Suppose we could create a number of levels, for example, say we had 8 voltages levels we could use 000 001 010 011 100 101 110 111

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Suppose we receive 011 000 100 111 000 001 110 010 011 000 100 111 000 001 110 010

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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 - 4000 Hz (3000 usable) If we use 2 signal levels MDR = 2 * 3000 * log2(2) = 6,000 bps

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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

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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

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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 ***

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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( 1 + 1000) = 3000 * log2( 1001 ) = 30,000 (approximately) Regardless of the number of signals used

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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

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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

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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

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Modem Constellation

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Modems Standard BaudBit Modulation raterate Technique V.21 300300 FSK V.22 600600/1200 PSK V.22bis 600 1200/2400 QAM V.23 12001200 FSK V.32 24004800/9600 QAM/TCM V.34 240028,800 V.90 240056,000 V.92 240056,000

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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

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