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difx:difx-sfxc_comparison

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TC016A comparison

This test makes use of a 128 Mbps VLBA observation from June 2009, used to compare DiFX against the VLBA hardware correlator (VHWC) and to validate DiFX-2.0 vs DiFX-1.5. The test below used about 2 seconds of data on 4C39.25 (exactly 2 for SFXC and DiFX, and 2.09s for VHWC). Below, a summary of results from FRING in AIPS for DiFX vs VHWC vs SFXC (with various windowing and spectral averaging) is reported.

The columns FRING:X/Y in the table below refers to the S/N reported by FRING for antenna X, polarisation Y.

Correlator run FRING 1/1 FRING 3/1 FRING 1/2 FRING 3/2 AVERAGE
DiFX 128→32 channels 432 428 365 364 397
VHWC 128→32 channels 481 476 376 378 427
SFXC 256→32 channels via lag (zero pad+Hann) 544 548 440 433 491
SFXC 256→32 channels via lag (zero pad) 608 616 460 455 534
SFXC 256→32 channels via lag (zero pad+Rect) 595 604 447 442 522
SFXC 256→32 channels via freq boxcar (zero pad+Hann) 422 424 358 352 389
SFXC 32 channels (zero pad+Hann) 520 523 415 411 467
SFXC 128 channels (zero pad+Hann) 628 631 553 545 589
SFXC 128→32 channels via AIPS (zero pad+Hann) 432 433 367 362 398
w/4 channel boxcar smoothing in FRING
DiFX 128→32 channels 669 664 554 553 610
VHWC 128→32 channels 689 683 520 521 603
SFXC 256→32 channels via lag (zero pad+Hann) 658 666 511 504 584
SFXC 256→32 channels via lag (zero pad) 663 676 478 473 572
SFXC 256→32 channels via lag (zero pad+Rect) 649 662 462 458 557
SFXC 256→32 channels via freq boxcar (zero pad+Hann) 652 657 539 529 594
SFXC 32 channels (zero pad+Hann) 642 649 500 494 571
SFXC 128 channels (zero pad+Hann) 848 851 694 685 769
SFXC 128→32 channels via AIPS (zero pad+Hann) 649 653 535 527 591

The bandpasses show that DiFX and VHWC are very similar, while SFXC is “smoother”. It looks like the channel response of SFXC is much wider, and hence that there is redundant information in adjacent channels, which is messing with the estimate of noise in FRING. Below are some plots that show delay/rate space for simulated data (very simple, no bandpass, no quantisation, zero relative delay, just pure white noise with a 0.05 correlation coefficient) that has been processed in a number of different ways:

This shows the result of a simple FFT, no zero padding, no windowing. The noise is flat everywhere.

This shows the result of a zero-padded FFT, no windowing. The peak is the same height, but the noise is marginally reduced.

This shows the result of windowed-overlapped FFT (Hamming window), no zero padding. The peak goes up but it is sitting on a plateau of higher noise. If you just estimate the noise globally, then the S/N seems higher, but if you use an estimate of the local noise in the vicinity of the peak, the S/N is the same.

This shows the result of windowed-overlapped FFT (Hamming window) with zero padding. Basically the same as the window-overlapped without zero padding.

But if you average the windowed/overlapped data, you're zooming in to a more representative area of the delay/rate space noise-wise, so the fringe is no longer sitting on a higher-noise plateau (relatively speaking).

So as you can see, the noise rolls off towards high lags when a Hamming window and overlapping is used rather than boxcar, as you expect. So if you estimate the noise globally, you get a lower value and hence higher S/N. But if you estimate the noise in the vicinity of the peak (in this case, near zero lag), it doesn't matter whether you zero pad or window-overlap, you get the same S/N as expected.

Here is a summary in table form (noise estimated by blanking the fringe and then taking the square root of the sum of the squared remaining points, global noise using all points, local noise using only +/- 10 lags):

Type of correlation signal / global noise signal / local noise
No overlap, straight FFT 16.06 15.94
No overlapping, zero padding 18.55 16.33
Hanning window + overlap 21.58 15.87
Hanning window + overlap, zero padded 21.76 15.88
Hanning window + overlap, zero padded, averaged 4x in freq 17.37 15.94

So as you can see, the S/N estimated locally is always pretty comparable, even though the S/N estimated globally is 35% higher with a windowed overlap. Zero padding does help a little, but at the level of 2-3%.

difx/difx-sfxc_comparison.1447904147.txt.gz · Last modified: 2015/11/19 14:35 by adamdeller