1. Logarithms Log Review

2. Logarithms For example

3. Logarithms

4. Laws of Logarithms

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

6. the effect is to create harmonic interface at

7. cause –transmitter, receiver of intervening transmission system nonlinearity

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

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

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

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

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

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

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

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

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

17. Hartley-Shannon Law

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

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

20. Hartley-Shannon Law S = signal power (watts)

21. Hartley-Shannon Law k=boltzmans constant

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

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

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 &

25. Hartley-Shannon Law Find S S=-161.8 dbw

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

27. ADCs The SNR in (dB) is therefore where about