1. February 22, 2005Week 6 1 EE521 Analog and Digital Communications James K. Beard, Ph. D. jkbeard@temple.edu Tuesday, February 22, 2005 http://astro.temple.edu/~jkbeard/

2. Week 62 February 22, 2005 Attendance

3. Week 63 February 22, 2005 Essentials Text: Bernard Sklar, Digital Communications, Second Edition SystemView  Student version included with text  Trial version has 90-day timeout  I have a mini-CD for you – and permission from Eagleware/Elanix Office  E&A 348  Tuesday afternoons 3:30 PM to 4:30 PM & before class  MWF 10:30 AM to 11:30 AM Final Exam Scheduled  Tuesday, May 10, 6:00 PM to 8:00 PM  Here in this classroom

4. Week 64 February 22, 2005 Today’s Topics Quiz Review and the Take-Home Quiz SystemView Trial Version Term Projects Individual Conferences Discussion (as time permits)

5. Week 65 February 22, 2005 Quiz Overview Practice Quiz was from text homework  Problem 1.1 page 51  Problem 2.2 page 101  Problem 3.1 page 162 Quiz was similar  From homework problems  Modifications to problem statement and parameters

6. Week 66 February 22, 2005 Quiz timeline Quiz last week  Open book  Calculator  No notes (will allow notes for next quiz & final) Follow-up quiz announced at end of class  Take-home  Will require SystemView to complete  Will be deployed on Blackboard this week

7. Week 67 February 22, 2005 The Curve

8. Week 68 February 22, 2005 Scoring Template

9. Week 69 February 22, 2005 Problem 1 Energy vs. power signals  Section 1.2.4 pp 14-16  Energy signal – nonzero but finite energy  Power signal – nonzero but finite power Definitions, equation s(1.7) and (1.8)

10. Week 610 February 22, 2005 Problem 1 Equations Part (a) Part (b) Part (c) Part (d)

11. Week 611 February 22, 2005 Problem 1 Powers & Energies

12. Week 612 February 22, 2005 Energy Spectra Section 1.4 pp 19, 20 Autocorrellation of energy signal Power spectrum

13. Week 613 February 22, 2005 Problem 1 Power Spectra Section 1.4 pp. 19, 20 Autocorrelation of power signal Power spectrum

14. Week 614 February 22, 2005 Problem 1 Spectra

15. Week 615 February 22, 2005 Problem 2, The Block Diagram Naturally sampled low pass analog waveform Local Oscillator LPF

16. Week 616 February 22, 2005 Spectrum of Naturally Sampled Signal Shows Part I

17. Week 617 February 22, 2005 Problem 2 Part II – The Figure BW W BW – signal bandwidth W – maximum spectral spread

18. Week 618 February 22, 2005 Problem 2 Part 2 The signal x 1 (t) has a power spectrum Shifted left by k. f s The signal x 2 (t)  Has a power spectrum that is one of the replicas shown in the previous slide  Spectral distortion results from the slope of the natural sampling overall shape  Error and distortion are determined by’ Alising into the passband from the other spectral replicas Residual high frequency terms from the LPF stopband Within these errors, x 2 (t) is a scaled replica of x s (t) Within this and the PAM quantization, x s (t) is a replica of the input signal

19. Week 619 February 22, 2005 Problem 2 Part III (1 of 2) The minimum sample rate is 2. W  Lower sample rates will allow splatter to alias into the signal band  Signal will still be reproduced, with larger errors The LPF  Passband extends to BW/2  Stopband begins at f s -W/2

20. Week 620 February 22, 2005 Problem 2 Part III (2 of 2) For a natural sampling duty cycle of d  The minimum system sample rate for two samples is 2. f s /d  Using a system sample rate that is a multiple of f s Provides the same sampling for every gate Allows accuracy of natural sampling with lower system sample rates The sample rate  Determines the LPF transition band of f s -(W+BW)/2  Higher is better for filter cost/performance trade space The spectrum aliasing number k  Should be significantly smaller than 1/d  Avoid selecting spectrum near the null in natural sampling spectra

21. Week 621 February 22, 2005 Question 3 – The Block Diagram Bandpass signal Local Oscillator LPF 2 2 2

22. Week 622 February 22, 2005 Problem 3 Part I The output signal x O (t) is the bandpass signal x B (t) shifted down in frequency by f 0 For all-analog signals, the LPF  Will supplement the last I.F. filter  Can provide better performance than a bandpass filter For sampled signals, the LPF  Provides anti-aliasing filtering – suppression of spectral images  May allow decimation to sample rate near BW

23. Week 623 February 22, 2005 Question 3, Part II Considerations are similar to those of Question 2  In Question 2, natural sampling generated an array of bandpass signals  The complex rest of the circuit was a quadrature demodulator that selected one of the bandpass signals  The duty cycle is not a part of Question 3 Minimum sample rate is 2. W LPF  Bandpass to BW/2  Stopband begins at f s – W/2

24. Week 624 February 22, 2005 Problem 3 Part III Sample rates f s that alias f 0 to ±f s /4 Nyquist criteria, including spectral spread Lowest sample rate is for a k of

25. Week 625 February 22, 2005 Problem III Part IV Look at numerical values of LPF specs  Bandpass to BW/2  Stopband begins at f s – W/2  Transition band is f s -(BW+W)/2  Shape factor is (2. f s -W)/BW LPF trade space is better for higher f s

26. Week 626 February 22, 2005 Problem 3 Part V The sample rate at I.F. is 2. W For complex signals, the Nyquist rate is W Allowing for a shape factor for the LPF increases the sample rate above 2. W Decimation  Minimum is a factor of 2 to produce a sample rate of W complex  Aliasing considerations can drive a complex data rate higher than W  Higher sample rates and simpler LPF will allow decimation of 3 or 4 to produce a complex sample rate near W  Dual-stage digital LPF can provide a very high performance – a shape factor only slightly larger than 1

27. Week 627 February 22, 2005 SystemView I have a mini-CD-ROM with the trial version When you install  During business hours  When asked for “Regular” or “Professional” select “Professional”  Call Maureen Chisholm at 678-218-4603 to get your activation code Other resources  The student version will probably carry you another week  The full version is available in E&A 604E – watch for two icons on the desktop and select the Professional version

28. Week 628 February 22, 2005 Term Projects Interpret, plan, model Use SystemView Assignments deployed by email last week Your preferences and comments are encouraged  Office hours  Email

29. Week 629 February 22, 2005 Individual Conferences Look at your term projects while you’re waiting your turn Stay when your turn is done Class will resume after individual conferences for discussion of term projects and SystemView

30. Week 630 February 22, 2005 Assignment Take-home quiz  Do the quiz you have  Print out the PDF file, these slides and go for 100% Do the input blocks to your Term Project in SystemView  Generate a signal  Add noise  Modulate  Set the clock  Run it and look at the time/frequency domains