1. TOW 2007: Correlator Theory Kerry Kingham - U.S. Naval Observatory Roger Cappallo – Haystack Observatory Mike Titus - Haystack Observatory

2. Outline Basic idea of how the correlator works Description of the Arcane (and Archaic) “Fringe Plot” Some idea of how problems affect the results

4. What Does a Correlator Do (and how does it do it)?

5. Why Correlate? If we had a high snr, we could just difference the arrival times (e.g. pulse) Unfortunately, quasar signals are ~10 3 weaker than the noise in our best receiving systems The correlater allows us to magically pull this weak signal out of the noise and measure its delay (and rate) between two sites

7. Cross-correlation of weak signals Let s(t) be a weak astronomical signal, and n 1 (t) and n 2 (t) be noise signals at sites 1 & 2

8. Correlation of weak signals (cont’d) Product of signals is: (s + n 1 ) (s + n 2 ) = s 2 + n 1 s + n 2 s + n 1 n 2

9. Summed Correlation Components

10. Correlation Hardware If done at the original RF, a delay model by itself would produce the correct Doppler shift Since we process at baseband, we need to have separate delay and phase models

11. Correlator Channel

12. Bandwidth Synthesis We measure delay by observing phase differences at different frequencies For a given delay, the higher the frequency, the greater the change in phase:

13. frequency phase (rot)

15. No good!

17. Optimizing Coherence In addition to the linear phase change due to frequency, there is a contribution to each channel’s phase from the instrumentation e.g. the filters in each VC have slightly different delays The phase cal subsystem injects tones into the front end every MHz with the same phase (at the start of each second). The correlator detects each tone, and adjusts the phase of the corresponding channel.

18. Phase-cal aligns the channels:

19. The Fringe Plot! (How a Mark IV Correlator person sees the results of correlation)

21. Top of the Plot in 3D! (Kashima style)

23. The Correlator as Spectrum Analyzer The correlator cross-correlates at many “lags”in the time domain If we have it autocorrelate (Gc to Gc rather than Gc to Ap) we get an autocorrelation function in delay (time). If we Fourier Transform the autocorrelation function in delay we transform the time function into a frequency function! We can turn the Correlator into a large, expensive, not very portable spectrum analyzer

24. Correlator as Spectrometer (cont)

25. Phase Cal as Test Tone Phase cal tones are injected early in the signal path They are excellent test signals as well as alignment tools At both the station and at the correlator, Pcal tones can be used as probes to investigate problems in the VLBI system

26. Analyzing Pcal Tones at the Correlator: Internal Spurious Signals Generated inside the VLBI System If at 1 Mhz or multiple and locked to the Maser, it can affect the phase cal amplitudes and phases Reflections of the Pcal tones are a common source of these signals

28. Signal Locked to Maser

29. Spurious Signal in Phase Cal

30. Reflected Signal

34. Spurious Signal amplitude > Phase Cal amplitude

35. Channel Spectra Showing Internal (?) RFI Signals

36. External Signals Not locked to maser Not necessarily at p-cal frequencies May be Time Dependent May be dependent on telescope direction

37. Early Scan RFI in “d” channel

38. A Few Minutes Later No RFI in “d” channel

39. Channel Spectra Good Channel (note p-cals): First Case: Bad RFISecond Case: Not so Bad RFI

40. Very External Signals Direct Digital Audio Broadcast Satellites –“XM” & “Sirius” over North America –Proposed service for Europe

41. “XM” Signals in N.A. Stations

42. References http://ivscc.gsfc.nasa.gov/publications/gm2000/whitney2 http://ivscc.gsfc.nasa.gov/publications/gm2004/kondo http://www.nrao.edu/php/sigpath/StaticHTML/correlator.ph phttp://www.nrao.edu/php/sigpath/StaticHTML/correlator.ph p http://www.cv.nrao.edu/vlbabook

43. End of Correlator Theory

46. Hardware and Software Structure...of current Mark IV correlator