1 / 27

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

elliotthernandez
Download Presentation

Logarithms

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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 • spikes, irregular pulses • Cause • lightning can severely alter data

  10. 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

  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=-161.8 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

More Related