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EE521 Analog and Digital Communications. James K. Beard, Ph. D. [email protected] Tuesday, February 22, 2005 http://astro.temple.edu/~jkbeard/. Attendance. Essentials. Text: Bernard Sklar, Digital Communications , Second Edition SystemView Student version included with text

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ee521 analog and digital communications

EE521 Analog and Digital Communications

James K. Beard, Ph. D.

[email protected]

Tuesday, February 22, 2005

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

Week 6

essentials
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
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
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 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
The Curve

Week 6

problem 1
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 equations
Problem 1 Equations
  • Part (a)
  • Part (b)
  • Part (c)
  • Part (d)

Week 6

energy spectra
Energy Spectra
  • Section 1.4 pp 19, 20
  • Autocorrellation of energy signal
  • Power spectrum

Week 6

problem 1 power spectra
Problem 1 Power Spectra
  • Section 1.4 pp. 19, 20
  • Autocorrelation of power signal
  • Power spectrum

Week 6

problem 2 part ii the figure
Problem 2 Part II – The Figure

BW

BW – signal bandwidth

W – maximum spectral spread

W

Week 6

problem 2 part 2
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
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
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

question 3 the block diagram

LPF

Bandpass signal

Local Oscillator

2

2

2

Question 3 – The Block Diagram

Week 6

problem 3 part i
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
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
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
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
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
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
Term Projects
  • Interpret, plan, model
  • Use SystemView
  • Assignments deployed by email last week
  • Your preferences and comments are encouraged
    • Office hours
    • Email

Week 6

individual conferences
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
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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