1. Timing Synchronization with Band Edge Filters
fred harris
11-15 September, 2017

2. What The Customer Wants

3. What the Customer Will Pay

4. When the Customer wants it.

5. The Size Customer Wants.

6. Timing and Carrier
Synchronization
of Digital Modems

7. Timing and Carrier Synchronization of Digital Modems
Momma’s Middle name is Synchronizer

8. A Common Line in Adventure Movies!

9. Find Peak of Correlation Function
Filter can’t answer the question:
“Am I standing at the highest level?”
She can only see the level where
you are standing.
A Better question to ask.
and one she can answer is:
“What’s the slope
where I am standing?”
Zero
Slope
Positive
Slope
Negative
Slope
f<fopt
f=fopt
f>fopt

10. Derivative with Help of Nearby Neighbors (Early and Late)

11. Maximizing Output of Correlation Receiver Same as Seeking Zero Derivative

12. To Determine Which Direction is the Peak of the Correlator, Qualify the Derivative with Polarity of the Correlator Output

14. Early-Late Gate Derivative

15. Combining Early and Late Gates in a One Derivative Filter

16. Slide Sampler to Input and Perform Timing Offset with Polyphase Digital Filter

18. We can do the same for phase offsets with a system that measures phase errors and adjusts a VCO to move the phase angle error towards 0. What is one to do when the phase offset is changing faster than the PLL can correct? You change loops to measure frequency offset and adjust VCO to move frequency error towards 0.

19. Frequency Matched Filter
Output Times
Derivative
Output

20. Time and Frequency Response, Matched Filter and Frequency Derivative Matched Filter

21. Frequency Matched Filter Non Data Aided Frequency Acquisition

22. Band Edge Filter

23. Spectra of Input Signal and Band Edge Filter Outputs

24. Frequency Locked Loop with Band Edge Filters
Maximum
Likelihood
Minimum
Variance

25. Frequency Locked PLL

26. Spectra of Signals From Band Edges Combined to form Two New Signals

27. Conjugate Product of Sum and Difference Band Edge Filters
Imaginary Part,
Sinusoid at Symbol Frequency.
Phase Related to Time offset
between Samples and Signal.
Real Part
DC Proportional to
Energy Difference

28. Equivalent Band Edge Options for Frequency Lock Loop

36. Eye Diagrams of Matched Filter, Band-Edge Filter Sum, Difference, and Product

37. Eye Diagrams of Matched Filter, Band-Edge Filter Sum,
Difference, and Product with Timing Offset

38. Spectra of SQRT Nyquist Shaped Modulation Signals over Range of Excess BW

39. Eye Diagrams Matched Filter Output

41. Cyclostationary Mean and Variance Eye Diagrams Magnitude Matched Filter Output

42. Spectral Lines from Excess BW: MF(t) x dMF(t)*
Modulation Noise

43. Eye Diagrams Band Edge Difference Filter Output

46. Cyclostationary Mean and Variance Eye Diagrams Magnitude Band Edge Difference Filter

47. Spectra of BEsum(t) x BEdiff(t)*
No Modulation Noise)

52. Homework Problem

53. Band Edge Filter Carrier Frequency and Timing Acquisition
4-samples per symbol

54. Band Edge Filter Carrier Frequency and Timing Acquisition
2-samples per symbol

58. Gardner Loop (MINL) Timing Error Detector
Timing Error(n) =[ydet(n-1)-ydet(n+1)]y(n)

59. Gardner Loop Track Zero Crossings y ydot = 0 when y = 0
Timing Error(n) =[ydet(n-1)-ydet(n+1)]y(n)

83. That’s all Folks

86. SOFTWARE
DEFINED
RADIO
MAN
Is Open For Questions