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Logarithms Log Review

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Logarithms For example

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Logarithms

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Laws of Logarithms

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Intermodulation noise –results when signals at different frequencies share the same transmission medium

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the effect is to create harmonic interface at

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cause –transmitter, receiver of intervening transmission system nonlinearity

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Crosstalk –an unwanted coupling between signal paths. i.e hearing another conversation on the phone Cause –electrical coupling

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Impluse noise –spikes, irregular pulses Cause –lightning can severely alter data

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Channel Capacity –transmission data rate of a channel (bps) Bandwidth –bandwidth of the transmitted signal (Hz) Noise –average noise over the channel Error rate –symbol alteration rate. i.e. 1-> 0

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Channel Capacity if channel is noise free and of bandwidth W, then maximum rate of signal transmission is 2W This is due to intersymbol interface

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Channel Capacity Example w=3100 Hz C=capacity of the channel c=2W=6200 bps (for binary transmission) m = # of discrete symbols

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Channel Capacity doubling bandwidth doubles the data rate if m=8

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Channel Capacity doubling the number of bits per symbol also doubles the data rate (assuming an error free channel) (S/N):-signal to noise ratio

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Hartley-Shannon Law Due to information theory developed by C.E. Shannon (1948) C:- max channel capacity in bits/second w:= channel bandwidth in Hz

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Hartley-Shannon Law Example W=3,100 Hz for voice grade telco lines S/N = 30 dB (typically) 30 dB =

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Hartley-Shannon Law

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Represents the theoretical maximum that can be achieved They assume that we have AWGN on a channel

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Hartley-Shannon Law C/W = efficiency of channel utilization bps/Hz Let R= bit rate of transmission 1 watt = 1 J / sec =enengy per bit in a signal

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Hartley-Shannon Law S = signal power (watts)

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Hartley-Shannon Law k=boltzmans constant

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Hartley-Shannon Law assuming R=W=bandwidth in Hz In Decibel Notation:

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Hartley-Shannon Law S=signal power R= transmission rate and -10logk=228.6 So, bit rate error (BER) for digital data is a decreasing function of For a given, S must increase if R increases

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Hartley-Shannon Law Example For binary phase-shift keying =8.4 dB is needed for a bit error rate of let T= k = noise temperature = C, R=2400 bps &

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Hartley-Shannon Law Find S S=-161.8 dbw

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ADCs typically are related at a convention rate, the number of bits (n) and an accuracy (+- flsb) for example –an 8 bit adc may be related to +- 1/2 lsb In general an n bit ADC is related to +- 1/2 lsb

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ADCs The SNR in (dB) is therefore where about

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