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### Transcript of Logarithms Log Review. Logarithms For example Logarithms

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Logarithms Log Review Slide 2 Logarithms For example Slide 3 Logarithms Slide 4 Laws of Logarithms Slide 5 Intermodulation noise results when signals at different frequencies share the same transmission medium Slide 6 the effect is to create harmonic interface at Slide 7 cause transmitter, receiver of intervening transmission system nonlinearity Slide 8 Crosstalk an unwanted coupling between signal paths. i.e hearing another conversation on the phone Cause electrical coupling Slide 9 Impluse noise spikes, irregular pulses Cause lightning can severely alter data Slide 10 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 Slide 11 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 Slide 12 Channel Capacity Example w=3100 Hz C=capacity of the channel c=2W=6200 bps (for binary transmission) m = # of discrete symbols Slide 13 Channel Capacity doubling bandwidth doubles the data rate if m=8 Slide 14 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 Slide 15 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 Slide 16 Hartley-Shannon Law Example W=3,100 Hz for voice grade telco lines S/N = 30 dB (typically) 30 dB = Slide 17 Hartley-Shannon Law Slide 18 Represents the theoretical maximum that can be achieved They assume that we have AWGN on a channel Slide 19 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 Slide 20 Hartley-Shannon Law S = signal power (watts) Slide 21 Hartley-Shannon Law k=boltzmans constant Slide 22 Hartley-Shannon Law assuming R=W=bandwidth in Hz In Decibel Notation: Slide 23 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 Slide 24 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 & Slide 25 Hartley-Shannon Law Find S S=-161.8 dbw Slide 26 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 Slide 27 ADCs The SNR in (dB) is therefore where about