Logarithms Log Review Logarithms For example Logarithms Logarithms

Logarithms • Log Review

Logarithms • For example

Logarithms

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 • 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 2 W • This is due to intersymbol interface

Channel Capacity • Example w=3100 Hz C=capacity of the channel c=2 W=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 d. B (typically) 30 d. B =

Hartley-Shannon Law

Hartley-Shannon Law • Represents 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=boltzman’s constant

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

Hartley-Shannon Law S=signal power R= transmission rate and -10 logk=228. 6 So, bit rate error (BER) for digital data is a decreasing function of For a given if R increases , S must increase

Hartley-Shannon Law • Example For binary phase-shift keying =8. 4 d. B 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

ADC’s • 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

ADC’s • The SNR in (d. B) is therefore where about