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### EE521 Analog and Digital Communications

James K. Beard, Ph. D.

Tuesday, February 22, 2005

http://astro.temple.edu/~jkbeard/

Week 6

Attendance

Week 6

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

Week 6

Today’s Topics

- Quiz Review and the Take-Home Quiz
- SystemView Trial Version
- Term Projects
- Individual Conferences
- Discussion (as time permits)

Week 6

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

Week 6

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

Week 6

The Curve

Week 6

Scoring Template

Week 6

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)

Week 6

Problem 1 Spectra

Week 6

Problem 2 Part 2

- The signal x1(t) has a power spectrum Shifted left by k.fs
- The signal x2(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, x2(t) is a scaled replica of xs(t)
- Within this and the PAM quantization, xs(t) is a replica of the input signal

Week 6

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 fs-W/2

Week 6

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.fs/d
- Using a system sample rate that is a multiple of fs
- 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 fs-(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

Week 6

Problem 3 Part I

- The output signal xO(t) is the bandpass signal xB(t) shifted down in frequency by f0
- 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

Week 6

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 fs – W/2

Week 6

Problem 3 Part III

- Sample rates fs that alias f0 to ±fs/4
- Nyquist criteria, including spectral spread
- Lowest sample rate is for a k of

Week 6

Problem III Part IV

- Look at numerical values of LPF specs
- Bandpass to BW/2
- Stopband begins at fs – W/2
- Transition band is fs-(BW+W)/2
- Shape factor is (2.fs-W)/BW
- LPF trade space is better for higher fs

Week 6

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

Week 6

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

Week 6

Term Projects

- Interpret, plan, model
- Use SystemView
- Assignments deployed by email last week
- Your preferences and comments are encouraged
- Office hours

Week 6

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

Week 6

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

Week 6

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