Logarithms Log Review

Logarithms For example

Logarithms

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 =

Hartley-Shannon Law

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= 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