2. InformationsourcePulsegeneratorTransfilterchannel (X(t (X(t (X T (t (X T (t Timing Receiverfilter Clockrecoverynetwork A/D + Channel noise Channel noisen(t) Output Block diagram of an Binary/M-ary signaling scheme+ H T (f) H R (f) Y(t) H c (f)

3. Informationsource TransmitterTransmitter Channel ReceiverReceiver Decision Communication system

5. InformationsourcePulsegeneratorTransfilter (X(t (X(t (X T (t Timing Block diagram Description H T (f) {d k }={1,1,1,1,0,0,1,1,0,0,0,1,1,1} TbTbTbTb TbTbTbTb TbTbTbTb TbTbTbTb For b k =1 For b k =0

6. InformationsourcePulsegeneratorTransfilter (X(t (X(t (X T (t Timing Block diagram Description (Continue - 1) Block diagram Description (Continue - 1) H T (f) {d k }={1,1,1,1,0,0,1,1,0,0,0,1,1,1} TbTbTbTb TbTbTbTb TbTbTbTb For b k =1 For b k =0 Transmitterfilter TbTbTbTb TbTbTbTb

7. InformationsourcePulsegeneratorTransfilter (X(t (X(t (X T (t Timing Block diagram Description (Continue - 2) Block diagram Description (Continue - 2) H T (f) {d k }={1,1,1,1,0,0,1,1,0,0,0,1,1,1} TbTbTbTb TbTbTbTb 100110 2T b 3T b 4T b 5T b t 6T b

8. InformationsourcePulsegeneratorTransfilter (X(t (X(t (X T (t Timing Block diagram Description (Continue - 3) H T (f) {d k }={1,1,1,1,0,0,1,1,0,0,0,1,1,1} TbTbTbTb TbTbTbTb 100110 2T b 3T b 4T b 5T b t 6T b TbTbTbTb 2T b 3T b 4T b 5T b t 6T b

9. Informationsource PulsegeneratorTransfilter (X(t (X(t Timing Block diagram Description (Continue - 4) H T (f) TbTbTbTb 2T b 3T b 4T b 5T b t 6T b TbTbTbTb 2T b 3T b 4T b 5T b t 6T b Channel noise n(t) Channel noise n(t) + t Receiverfilter H R (f)

10. Block diagram Description (Continue - 5) TbTbTbTb 2T b 3T b 4T b 5T b t 6T b TbTbTbTb 2T b 3T b 4T b 5T b t 6T b t

11. InformationsourcePulsegeneratorTransfilterchannel (X(T (X(T (X t (T (X t (T Timing Receiverfilter Clockrecoverynetwork A/D + Channel noise Channel noisen(t) Output Block diagram of an Binary/M-ary signaling scheme+ H T (f) H R (f) Y(t) H c (f)

12. Block diagram Description TbTbTbTb 2T b 3T b 4T b 5T b t 6T b TbTbTbTb 2T b 3T b 4T b 5T b t 6T b t 1 0 0 0 1 0 1 0 0 0 1 0 1 0 0 1 1 0 1 0 0 1 1 0 t

13. InformationsourcePulsegeneratorTransfilterchannel (X(t (X(t (X T (t (X T (t Timing Receiverfilter Clockrecoverynetwork A/D + Channel noise Channel noisen(t) Output Block diagram of an Binary/M-ary signaling scheme+ H T (f) H R (f) Y(t) H c (f)

14. Transfilterchannel P g (t) P g (t) Receiverfilter Explanation of P r (t) H T (f) H R (f) H c (f) P r (t) P r (t) H T (f) H c (f) H R (f) P g (f) P g (f) P r (f) P r (f)

15. The output of the pulse generator X(t),is given by P g (t) is the basic pulse whose amplitude a k depends on.the k th input bit

16. For t m =mT b +t d and t d is the total time delay in the system, we get. t t t t1t1t1t1 t2t2t2t2 t3t3t3t3 tmtmtmtm The input to the A/D converter is

17. t t1t1t1t1 t2t2t2t2 t3t3t3t3 tmtmtmtm The output of the A/D converter at the sampling time t m =mT b +t d TbTbTbTb 2T b 3T b 4T b 5T b t 6T b

18. t t1t1t1t1 t2t2t2t2 t3t3t3t3 tmtmtmtm ISI - Inter Symbol Interference

19. Transfilterchannel P g (t) P g (t) Receiverfilter Explanation of ISI H T (f) H R (f) H c (f) P r (t) P r (t) P g (f) P g (f) P r (f) P r (f) TransfilterchannelReceiverfilter H T (f) H R (f) H c (f) t f FourierTransform BandPassFilter f FourierTransform t

20. Explanation of ISI - Continue t f FourierTransform BandPassFilter f FourierTransform t TbTbTbTb 2T b 3T b 4T b 5T b t 6T b

21. -The pulse generator output is a pulse waveform If k th input bit is 1 if k th input bit is 0 -The A/D converter input Y(t)

22. -The pulse generator output is a pulse waveform If k th input bit is 1 if k th input bit is 0 -The A/D converter input Y(t)

23. 5.2 BASEBAND BINARY PAM SYSTEMS - minimize the combined effects of inter symbol interference and noise in order to achieve minimum probability of error for given data rate.

24. 5.2.1 Baseband pulse shaping The ISI can be eliminated by proper choice of received pulse shape p r (t). Doe’s not Uniquely Specify Pr(t) for all values of t.

25. Theorem Proof To meet the constraint, Fourier Transform Pr(f) of Pr(t), should satisfy a simple condition given by the following theorem

26. Which verify that the Pr(t) with a transform Pr(f) Satisfy ZERO ISI

27. The condition for removal of ISI given in the theorem is called Nyquist (Pulse Shaping) Criterion TbTbTbTb 2Tb2Tb2Tb2Tb -Tb-Tb-Tb-Tb -2T b 1

28. The Theorem gives a condition for the removal of ISI using a Pr(f) with a bandwidth larger then rb/2/. ISI can’t be removed if the bandwidth of Pr(f) is less then rb/2. H T (f) H c (f) H R (f) P g (f) P g (f) P r (f) P r (f) TbTbTbTb 2T b 3T b 4T b 5T b t 6T b

29. Particular choice of Pr(t) for a given application The smallest values near Tb, 2Tb, … In such that timing error (Jitter) will not Cause large ISI will not Cause large ISI Shape of Pr(f) determines the ease with which shaping filters can be realized.

30. A Pr(f) with a smooth roll - off characteristics is preferable over one with arbitrarily sharp cut off characteristics. Pr(f) Pr(f)