Testing the effective bandwidth of ALMA data channels

1. Baseline Correlator

Richard Hills' Note on Spectral Response (April 2012) includes a prediction of the FWHM and effective channel bandwidth as a function two choices: the correlator window function (Uniform, Cosine, Hanning (i.e. Cosine squared), and Welch) and the degree of subsequent online channel averaging (N=1,2,4,8). Here we attempt to test these predictions on real ALMA data, by letting the clean task effectively perform offline channel averaging by a controlled amount, and analyzing the noise in the resulting images. Due to the good match that we found, we filed PREQ-320 and ICT-2542 so that Cycle 3 data will have these values correctly written to the appropriate columns of the ASDM and hence the ms.

These tests were performed on Band 3 dataset: uid___A002_Xa5534d_X8bc, observed on 2015-07-10 04:37:44 UT in software version 2014.6 (the Cycle 3 candidate). It had Hanning smoothing applied online to all spws (like virtually every ALMA dataset) and no channel averaging. The data were calibrated by C. Brogan using the manual script generator. T. Hunter performed the imaging and analysis. The bandpass calibrator and polarization calibrator were both too strong (6 Jy) such that their images would have been dynamic range limited. Instead, the phase calibrator (field 3, J1832-2039, F_nu=0.45 Jy) was imaged in spw='0' (TDM=128 channels, spw=17 in the raw data) centered at 95.166 GHz. It was observed in 10 scans: 14, 16, 19, 22, 24, 26, 30, 36, 38, 39, for a total on-source time of 5.039 minutes, according to au.timeOnSource executed on the raw data file. The median Tsys in spw 17 reported by au.medianTsysForField over the 4 Tsys scans (13, 21, 29, 35) acquired on the phase calibrator is 46.35 K, while the mean is 46.32 K. Using these values, the predicted rms for a single TDM channel, using the effective bandwidth of 2.667 channels for Hanning smoothed data, and the equation for sigma_image from DataWeightsAndCombination for 630 baselines (from 36 12m antennas) is: 0.4529 mJy, computed as follows:
CASA <17>: 2 * 1.3806488e-23 * 46.35 * 1e26 / (.95*.88*.75*pi*6**2) / (630 * 2.6676 * 15.625e6 * 2 * 5.039*60)**0.5
  Out[17]: 0.0004529
This value is within 1% of the achieved rms in a single channel! (see Test 1 below)

Tests of Hann window with different values of Channel averaging

Test 1

In the first test, only one group of N contiguous channels was imaged. This test is potentially affected by differing uv coverage since the larger values of N span significantly more uv space. The SNR is the peak intensity in the image divided by the standard deviation of the pixels in a rectangular box located north of the target blc=333,429, trc=473,407. The standard deviation was also measured in a second box (south of the target), and the mean of the two values was used.

Nchan Channels SNR St.Dev. (sigma) in 2 boxes (mJy/beam) Mean sigma (mJy/beam) Ratio: mean_sigma_1/mean_sigma_N Ratio^2 Richard's prediction for effective BW Richard's prediction for Ratio^2 Error in Richard's prediction Sigma_image prediction (mJy/b) Error in Sigma_image equation prediction
1 63~63 1051 0.4373, 0.4607 0.4490 1.000 1.000 2.667 1.000 n/a 0.4529 +0.8%
2 63~64 1134 0.4052, 0.4186 0.4119 1.090 1.188 3.200 1.200 +1.0% 0.4135 +0.4%
4 61~64 1378 0.3323, 0.3399 0.3361 1.336 1.785 4.923 1.846 +3.4% 0.3334 -0.8%
8 59~66 1778 0.2572, 0.2575 0.2573 1.745 3.045 8.828 3.310 +8.7% 0.2490 -3.2%
16 55~70 2405 0.1914, 0.1880 0.1897 2.367 5.602 n/a (16) n/a (6.0) n/a 0.1849 -2.5%

Test 2

In the second test, seven separated groups of N contiguous channels were imaged. This test should be more immune to uv coverage effects. The gap between the 8-channel wide bins was 2 channels, which should avoid effects of non-independent channels. Sigma was measured in only the one box north of the target.

Nchan Channels SNR St.Dev. (sigma) Ratio: sigma_1/sigma_N Ratio^2 Richard's prediction for Ratio^2 Error in prediction
7x1 30,40,50,60,70,80,90 2519 0.1819 1.000 1.000 1.000 n/a
7x2 30~31,40~41, etc. 2802 0.1635 1.113 1.238 1.200 -3.1%
7x4 30~33,40~43, etc. 3446 0.1330 1.368 1.871 1.846 -1.3%
7x8 30~37,40~47, etc. 4360 0.1050 1.732 3.001 3.310 +10%

Test 3

In the third (and perhaps best) test, seven separated groups of contiguous channels were imaged, but the minimum gap was increased from 2 to 3 channels, to better insure no effects from non-independent channels between neighboring groups. Image standard deviation was measured in the same 2 boxes as Test 1 and the two values were averaged. Results are similar to Test 1. The effective bandwidth for the case of N=8 seems to be overpredicted somewhat. For comparison, naively assuming an effective bandwidth of 8.0 channels for N=8 (i.e. predicted ratio of 2.828) would underpredict the effective bandwidth by 4% (Test 3) to 7% (Test 1).

Nchan Channels SNR St.Dev. (sigma) in two boxes Mean sigma Ratio: mean_sigma_1/mean_sigma_N Ratio^2 Richard's prediction for Ratio^2 Percent error in prediction
7x1 28,39,50,61,72,83,94 2603 0.1761, 0.1772 0.17665 1.000 1.000 1.000 n/a
7x2 28~29,39~40, etc. 2874 0.1595, 0.1605 0.16000 1.104 1.219 1.200 -1.6%
7x4 28~31,39~42, etc. 3516 0.1303, 0.1255 0.12790 1.381 1.908 1.846 -3.2%
7x8 28~35,39~46, etc. 4340 0.1056, 0.0999 0.10275 1.719 2.956 3.310 +12%

Test of different window functions with N=1

On October 5, 2010, a short observation of J1924-292 was made with all 7 window functions observed in succession in scan 2 (CSV-494). Here I have split out this scan and run statwt(spw='1:12~116') on each of the four TDM spws (1,3,5,7). I then compare the resulting weights with Richard's prediction for effective bandwidth, which should scale linearly. The script that generated the output below is attached to this page.
WindowFctn name    medianRatioToUniform  HillsPredict  PercentError
Blackmann_Harris         3.340            3.877       16
         Uniform         1.000             1.000       0
         Hanning         2.283             2.667       17
         Hamming         2.057             2.516       22
        Bartlett         2.558             3.000       17
       Blackmann         2.597             3.283       26
           Welch         1.504             1.874       25
-------------------------------------------------------------------------------------------------------
WindowFctn name  Spw Pol medianWt  ratioToUniform  HillsPredict  PercentError
Blackmann_Harris  1  0    114548     3.471        3.877   12
         Uniform  1  0     33001     1.000       1.000    0
         Hanning  1  0     74850     2.268       2.667   18
         Hamming  1  0     68333     2.071       2.516   22
        Bartlett  1  0     85791     2.600       3.000   15
       Blackmann  1  0     92254     2.795       3.283   17
           Welch  1  0     49520     1.501       1.874   25
Blackmann_Harris  1  1     92488     3.210       3.877   21
         Uniform  1  1     28817     1.000       1.000   0
         Hanning  1  1     49105     1.704       2.667   57
         Hamming  1  1     46728     1.622       2.516   55
        Bartlett  1  1     61150     2.122       3.000   41
       Blackmann  1  1     60574     2.102       3.283   56
           Welch  1  1     36431     1.264       1.874   48
Blackmann_Harris  3  0     98516     2.328       3.877   67
         Uniform  3  0     42320     1.000       1.000   0
         Hanning  3  0     82184     1.942       2.667   37
         Hamming  3  0     81057     1.915       2.516   31
        Bartlett  3  0     97835     2.312       3.000   30
       Blackmann  3  0     98124     2.319       3.283   42
           Welch  3  0     61203     1.446       1.874   30
Blackmann_Harris  3  1     11021     3.886       3.877   -0
         Uniform  3  1      2836     1.000       1.000   0
         Hanning  3  1      7111     2.507       2.667   6
         Hamming  3  1      6566     2.315       2.516   9
        Bartlett  3  1      9088     3.204       3.000   -6
       Blackmann  3  1      8584     3.026       3.283   8
           Welch  3  1      5170     1.823       1.874   3
Blackmann_Harris  5  0     55353     2.985       3.877   30
         Uniform  5  0     18542     1.000       1.000   0
         Hanning  5  0     42622     2.299       2.667   16
         Hamming  5  0     37888     2.043       2.516   23
        Bartlett  5  0     46666     2.517       3.000   19
       Blackmann  5  0     44479     2.399       3.283   37
           Welch  5  0     27954     1.508       1.874   24
Blackmann_Harris  5  1     26167     2.485       3.877   56
         Uniform  5  1     10529     1.000       1.000   0
         Hanning  5  1     18857     1.791       2.667   49
         Hamming  5  1     18868     1.792       2.516   40
        Bartlett  5  1     21179     2.012       3.000   49
       Blackmann  5  1     17728     1.684       3.283   95
           Welch  5  1     12621     1.199       1.874   56
Blackmann_Harris  7  0     21292     4.318       3.877   -10
         Uniform  7  0      4931     1.000       1.000   0
         Hanning  7  0     13569     2.752       2.667   -3
         Hamming  7  0     14214     2.883       2.516   -13
        Bartlett  7  0     25034     5.077       3.000   -41
       Blackmann  7  0     18188     3.688       3.283   -11
           Welch  7  0     11317     2.295       1.874   -18
Blackmann_Harris  7  1     20843     6.748       3.877   -43
         Uniform  7  1      3089     1.000       1.000   0
         Hanning  7  1     11000     3.562       2.667   -25
         Hamming  7  1      9306     3.013       2.516   -17
        Bartlett  7  1     15170     4.912       3.000   -39
       Blackmann  7  1     14787     4.788       3.283   -31
           Welch  7  1      6827     2.210       1.874   -15

2. ACA Correlator (with Cycle 2 frequency profile synthesis)

The ACA correlator uses frequency profile synthesis (FPS) to emulate the spectral resolution profile of the baseline correlator (see ALMA Memo 580). In effect, the ACA FPS synthesizes “a XF freq-response convolved with Hanning window function” from linear combinations of “FX freq-responses. But what does FPS do to the effective bandwidth of a single channel? Is it more or less than the 2.667 factor described in Richard's memo? The FPS appears to draw from 12 FX channels to produce a spectrum with 6 output channels. Therefore, we might expect the effective bandwidth of 1 FPS output channel to differ from the BL correlator value of 2.667 channels. We also expect that the difference may be a function of the online-binning factor N. To test this hypothesis, we did similar imaging tests with ACA data, equivalent to Test 1 and Test 3 above on the BL correlator data. We chose two Band 3 Cycle 2 science projects, and imaged the phase calibrator in one execution of each project using CASA 4.6.151 and a TDM-like spw (124 channels). We cleaned to a threshold of 2*im.apparentsens, using the same mask for all images. The sigma values below were all measured using the mask parameter of imstat, setting it to the annular region between the primary beam response level of 0.5 and 0.8.

In a separate test, the benchmark imaging report on Cycle 2 data (attached to CAS-8390) shows (Fig. 11) that the ratio of the achieved rms to the expected rms (using ia.apparentsens) in spectral cubes is too low by about 15%, while the rms in continuum images is about right. This could be explained if the expected rms per channel is too high, which could be the case if the effective noise bandwidth is wider than the baseline correlator. The line and continuum results would be simultaneously explained if the effective noise bandwidth is about 30% wider when averaging 1 to a few channels, with the effect lessening to the physical bandwidth as more channels are combined. This trend is exactly what is seen in the Low S/N case below.

High S/N case

The first dataset was uid___A002_X9dcf39_X3085 (April 10, 2015), which has a per-channel S/N of 209 on the phase calibrator J1717-3342. It likely becomes dynamic range limited for large values of Nchan. Although Richard did not calculate a value for Nchan=16, the nominal value is 6.0 assuming that the overlap effect is negligible for Nchan this large.

Nchan Channels Peak (Jy/b) Sigma in
annulus (Jy)
SNR Sigma Ratio
(Sigma1/SigmaN)
Ratio^2 Richard's prediction
for Ratio^2
Sigma
discrepancy
SigmaAsens
Corrected (Jy)
SigmaAsens
Discrepancy
1 63~63 1.03873 0.00566 183.39 1.0000 1.0000 1.0000   0.00553 2.47%
2 63~64 1.04018 0.00489 212.57 1.1575 1.3399 1.2000 -5.36% 0.00505 -3.01%
4 61~64 1.03764 0.00404 256.56 1.4005 1.9614 1.8460 -2.99% 0.00407 -0.56%
8 59~66 1.03584 0.00310 333.92 1.8259 3.3340 3.3100 -0.36% 0.00304 2.14%
16 55~70 1.03385 0.00245 422.51 2.3148 5.3583 n/a (6.0) 5.82% 0.00226 8.37%

The result of Test 3 is:

Nchan Channels Peak (Jy/b) Sigma in
annulus (Jy/b)
SNR Sigma Ratio
(Sigma1/SigmaN)
Ratio^2 Richard's prediction
for Ratio^2
Sigma
discrepancy
SigmaAsens
Corrected (Jy/b)
SigmaAsens
Discrepancy
1 20~20;34~34;48~48;62~62;76~76;90~90 1.03008 0.00241 427.99 1.0000 1.0000 1.0000   0.00368 -34.67%
2 20~21;34~35;48~49;62~63;76~77;90~91 1.02895 0.00178 578.58 1.3534 1.8316 1.2000 -19.06% 0.00260 -31.73%
4 20~23;34~37;48~51;62~65;76~79;90~93 1.02915 0.00145 712.03 1.6652 2.7729 1.8460 -18.41% 0.00185 -21.72%
8 20~27;34~41;48~55;62~69;76~83;90~97 1.02970 0.00144 714.23 1.6694 2.7870 3.3100 8.98% 0.00131 10.41%

These results are mixed. For values of Nchan>4, the improvement in sensitivity with Nchan is worse than expected, while for Nchan=2,4, it is better than expected. However, the absolute sensitivity is closest to CASA's im.apparentsens (corrected for BLC-like behavior) for the largest value of Nchan.

Moderate S/N case:

The second project was 2013.1.00356.S and execution uid___A002_X9f15bd_X31e9 (April 25, 2015) which used phasecal J0058-5219 with per-channel S/N=18, which should not become dynamic range limited with any value of Nchan. Here we include the value of CASA's im.apparentsens method (column = SigmaAsens "Corrected"), which computes the expected rms based on the real data weights and flags. In Cycle 2 data, it does not know about the effective bandwidth so it uses the physical channel width. Thus, we have corrected the values here using the factors derived by Richard for the BL correlator.

The Test 1 result is:
Nchan Channels Peak (Jy/b) Sigma in
annulus (Jy)
SNR Sigma Ratio
(Sigma1/SigmaN)
Ratio^2 Richard's prediction
for Ratio^2
Sigma
discrepancy
SigmaAsens
Corrected (Jy)
SigmaAsens
Discrepancy
1 63~63 0.07653 0.00450 17.01 1.0000 1.0000 1.0000   0.00461 -2.33%
2 63~64 0.08113 0.00406 20.01 1.1094 1.2308 1.2000 -1.26% 0.00421 -3.56%
4 61~64 0.07764 0.00324 23.94 1.3871 1.9241 1.8460 -2.05% 0.00339 -4.33%
8 59~66 0.08166 0.00257 31.80 1.7518 3.0688 3.3100 3.86% 0.00253 1.44%
16 55~70 0.08073 0.00205 39.39 2.1952 4.8190 n/a (6.0) 11.58% 0.00188 8.84%

The Test 3 result is:
Nchan Channels Peak (Jy/b) Sigma in
annulus (Jy/b)
SNR Sigma Ratio
(Sigma1/SigmaN)
Ratio^2 Richard's prediction
for Ratio^2
Sigma
discrepancy
SigmaAsens
Corrected (Jy/b)
SigmaAsens
Discrepancy
1 20~20;34~34;48~48;62~62;76~76;90~90 0.07890 0.00194 40.76 1.0000 1.0000 1.0000   0.00307 -36.97%
2 20~21;34~35;48~49;62~63;76~77;90~91 0.07832 0.00179 43.69 1.0796 1.1656 1.2000 1.46% 0.00217 -17.51%
4 20~23;34~37;48~51;62~65;76~79;90~93 0.07814 0.00153 51.20 1.2683 1.6086 1.8460 7.13% 0.00154 -0.81%
8 20~27;34~41;48~55;62~69;76~83;90~97 0.07782 0.00118 65.70 1.6342 2.6707 3.3100 11.33% 0.00109 9.00%

The improvement in sensitivity with Nchan matches expectation for N=2, but is a worse match for N=4,8. The absolute sensitivity most closely matches the prediction for BLC correlator for Nchan=4.

Low SNR case

Using the first field (5) of the science target produces no detection.

The Test 1 result is:
Nchan Channels Peak (Jy/b) Sigma in
annulus (Jy)
SNR Sigma Ratio
(Sigma1/SigmaN)
Ratio^2 Richard's prediction
for Ratio^2
Sigma
discrepancy
SigmaAsens
Corrected (Jy)
SigmaAsens
Discrepancy
1 63~63 0.04119 0.00987 4.17 1.0000 1.0000 1.0000   0.01013 -2.57%
2 63~64 0.03948 0.00844 4.68 1.1700 1.3689 1.2000 -6.37% 0.00925 -8.78%
4 61~64 0.02603 0.00685 3.80 1.4405 2.0750 1.8460 -5.68% 0.00747 -8.26%
8 59~66 0.02140 0.00494 4.33 1.9975 3.9901 3.3100 -8.92% 0.00559 -11.53%
16 55~70 0.01566 0.00382 4.10 2.5862 6.6885 6.0000 -5.29% 0.00414 -7.79%

The Test 3 result is:
Nchan Channels Peak (Jy/b) Sigma in
annulus (Jy)
SNR Sigma Ratio
(Sigma1/SigmaN)
Ratio^2 Richard's prediction
for Ratio^2
Sigma
discrepancy
SigmaAsens
Corrected (Jy)
SigmaAsens
Discrepancy
1 20~20;34~34;48~48;62~62;76~76;90~90 0.01289 0.00425 3.04 1.0000 1.0000 1.0000   0.00691 -38.60%
2 20~21;34~35;48~49;62~63;76~77;90~91 0.01160 0.00382 3.03 1.1111 1.2346 1.2000 -1.41% 0.00491 -22.12%
4 20~23;34~37;48~51;62~65;76~79;90~93 0.00856 0.00305 2.81 1.3932 1.9409 1.8460 -2.47% 0.00347 -12.24%
8 20~27;34~41;48~55;62~69;76~83;90~97 0.00746 0.00226 3.30 1.8814 3.5395 3.3100 -3.30% 0.00246 -8.35%

3. ACA Correlator (with Cycle 3 frequency profile synthesis)

High S/N case

Dataset uid___A002_Xae4720_X57fe from project 2015.1.00665.S (observed 2015-Dec-28). Imaged phase calibrator J0854+2006 in spw 1 (128 channels). Unfortunately, it is quite bright, so these results are likely dynamic-range limited.

The Test 1 result is:
Nchan Channels Peak (Jy/b) Sigma in
annulus (Jy)
SNR Sigma Ratio
(Sigma1/SigmaN)
Ratio^2 Richard's prediction
for Ratio^2
Sigma
discrepancy
SigmaAsens
Corrected (Jy)
SigmaAsens
Discrepancy
1 63~63 3.44665 0.01727 199.58 1.0000 1.0000 1.0000   0.01267 36.29%
2 63~64 3.45214 0.01433 240.84 1.2048 1.4516 1.2000 -9.08% 0.01157 23.91%
4 61~64 3.46646 0.01677 206.71 1.0298 1.0605 1.8460 31.94% 0.00933 79.81%
8 59~66 3.46920 0.01356 255.88 1.2737 1.6224 3.3100 42.83% 0.00696 94.66%
16 55~70 3.46731 0.01158 299.39 1.4912 2.2236 n/a (6.0) 64.27% 0.00517 123.86%

The Test 3 result is:
Nchan Channels Peak (Jy/b) Sigma in
annulus (Jy)
SNR Sigma Ratio
(Sigma1/SigmaN)
Ratio^2 Richard's prediction
for Ratio^2
Sigma
discrepancy
SigmaAsens
Corrected (Jy)
SigmaAsens
Discrepancy
1 20~20;34~34;48~48;62~62;76~76;90~90 3.45521 0.00784 440.76 1.0000 1.0000 1.0000   0.00668 17.37%
2 20~21;34~35;48~49;62~63;76~77;90~91 3.45364 0.00683 505.69 1.1478 1.3175 1.2000 -4.56% 0.00472 44.61%
4 20~23;34~37;48~51;62~65;76~79;90~93 3.45336 0.00735 469.87 1.0666 1.1377 1.8460 27.38% 0.00334 120.09%
8 20~27;34~41;48~55;62~69;76~83;90~97 3.46488 0.00542 639.58 1.4470 2.0939 3.3100 25.73% 0.00236 129.34%

Moderate S/N case

Using the flux calibrator from the same dataset as above, it is much weaker, so less affected by the image dynamic range limit.

The Test 1 result is:
Nchan Channels Peak (Jy/b) Sigma in
annulus (Jy)
SNR Sigma Ratio
(Sigma1/SigmaN)
Ratio^2 Richard's prediction
for Ratio^2
Sigma
discrepancy
SigmaAsens
Corrected (Jy)
SigmaAsens
Discrepancy
1 63~63 0.74612 0.01859 40.13 1.0000 1.0000 1.0000   0.01267 46.74%
2 63~64 0.74688 0.01836 40.67 1.0125 1.0251 1.2000 8.20% 0.01157 58.75%
4 61~64 0.75373 0.01471 51.22 1.2637 1.5968 1.8460 7.52% 0.00933 57.77%
8 59~66 0.75689 0.01113 68.00 1.6705 2.7905 3.3100 8.91% 0.00696 59.82%
16 55~70 0.75894 0.00878 86.47 2.1185 4.4882 6.0000 15.62% 0.00517 69.65%

The Test 3 result is:
Nchan Channels Peak (Jy/b) Sigma in
annulus (Jy)
SNR Sigma Ratio
(Sigma1/SigmaN)
Ratio^2 Richard's prediction
for Ratio^2
Sigma
discrepancy
SigmaAsens
Corrected (Jy)
SigmaAsens
Discrepancy
1 63~63 0.74645 0.01764 42.32 1.0000 1.0000 1.0000   0.01091 61.74%
2 63~64 0.74701 0.01777 42.03 0.9924 0.9849 1.2000 10.38% 0.00995 78.55%
4 61~64 0.75398 0.01401 53.82 1.2591 1.5853 1.8460 7.91% 0.00803 74.57%
8 59~66 0.75697 0.01085 69.74 1.6251 2.6409 3.3100 11.95% 0.00599 81.13%
16 55~70 0.75894 0.00871 87.09 2.0242 4.0973 6.0000 21.01% 0.00445 95.77%

Low SNR case

Using the first science field (3) of the above dataset:

The Test 1 result is:
Nchan Channels Peak (Jy/b) Sigma in
annulus (Jy)
SNR Sigma Ratio
(Sigma1/SigmaN)
Ratio^2 Richard's prediction
for Ratio^2
Sigma
discrepancy
SigmaAsens
Corrected (Jy)
SigmaAsens
Discrepancy
1 63~63 0.03368 0.01043 3.23 1.0000 1.0000 1.0000   0.01009 3.33%
2 63~64 0.03017 0.00978 3.08 1.0657 1.1358 1.2000 2.79% 0.00921 6.20%
4 61~64 0.02777 0.00808 3.44 1.2900 1.6642 1.8460 5.32% 0.00743 8.82%
8 59~66 0.02178 0.00613 3.56 1.7017 2.8956 3.3100 6.92% 0.00555 10.47%
16 55~70 0.01612 0.00444 3.63 2.3463 5.5049 6.0000 4.40% 0.00412 7.87%

The Test 3 result is:
Nchan Channels Peak (Jy/b) Sigma in
annulus (Jy)
SNR Sigma Ratio
(Sigma1/SigmaN)
Ratio^2 Richard's prediction
for Ratio^2
Sigma
discrepancy
SigmaAsens
Corrected (Jy)
SigmaAsens
Discrepancy
1 20~20;34~34;48~48;62~62;76~76;90~90 0.02298 0.00576 3.99 1.0000 1.0000 1.0000   0.00532 8.36%
2 20~21;34~35;48~49;62~63;76~77;90~91 0.01774 0.00478 3.71 1.2052 1.4524 1.2000 -9.10% 0.00376 27.16%
4 20~23;34~37;48~51;62~65;76~79;90~93 0.01230 0.00338 3.64 1.7070 2.9139 1.8460 -20.41% 0.00266 26.96%
8 20~27;34~41;48~55;62~69;76~83;90~97 0.00674 0.00227 2.97 2.5421 6.4622 3.3100 -28.43% 0.00188 20.56%

-- ToddHunter - 2015-07-29
Topic attachments
I Attachment Action Size Date Who Comment
analyze.py.txttxt analyze.py.txt manage 2 K 2015-08-05 - 00:10 ToddHunter  
clean.py.txttxt clean.py.txt manage 3 K 2016-02-19 - 11:04 ToddHunter script used for the BL correlator imaging test
Topic revision: r12 - 2016-03-17, ToddHunter
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