1. Logarithms
Log Review

2. Logarithms
For example

3. Logarithms

4. Logarithms
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 Cause spikes, irregular pulses
lightning can severely alter data

10. Channel Capacity Channel Capacity Bandwidth Noise Error rate
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. Hartley-Shannon Law
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=boltzman’s 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= dbw

26. 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

27. ADC’s
The SNR in (dB) is therefore
where
about