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Logarithms Log Review
Logarithms For example
Laws of Logarithms
Intermodulation noise –results when signals at different frequencies share the same transmission medium
the effect is to create harmonic interface at
cause –transmitter, receiver of intervening transmission system nonlinearity
Crosstalk –an unwanted coupling between signal paths. i.e hearing another conversation on the phone Cause –electrical coupling
Impluse noise –spikes, irregular pulses Cause –lightning can severely alter data
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
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
Channel Capacity Example w=3100 Hz C=capacity of the channel c=2W=6200 bps (for binary transmission) m = # of discrete symbols
Channel Capacity doubling bandwidth doubles the data rate if m=8
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
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
Hartley-Shannon Law Example W=3,100 Hz for voice grade telco lines S/N = 30 dB (typically) 30 dB =
Represents the theoretical maximum that can be achieved They assume that we have AWGN on a channel
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
Hartley-Shannon Law S = signal power (watts)
Hartley-Shannon Law k=boltzmans constant
Hartley-Shannon Law assuming R=W=bandwidth in Hz In Decibel Notation:
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
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 &
Hartley-Shannon Law Find S S=-161.8 dbw
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
ADCs The SNR in (dB) is therefore where about
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