Differences
This shows you the differences between two versions of the page.
|
projects:mkat_sband:pub:snrdet [2020/10/27 20:12] wucknitz |
projects:mkat_sband:pub:snrdet [2020/11/04 11:13] (current) wucknitz |
||
|---|---|---|---|
| Line 12: | Line 12: | ||
| | 3 | symmetric diff in time | from difference to mean of both adjacent time bins | | | 3 | symmetric diff in time | from difference to mean of both adjacent time bins | | ||
| | 4 | symmetric diff in freq | from difference to mean of both adjacent channels | | | 4 | symmetric diff in freq | from difference to mean of both adjacent channels | | ||
| + | | 5 | weights | from ''WEIGHT_SPECTRUM'', derived from autocorrelations, dt*df/(auto1*auto2) | | ||
| + | | 6 | rms2 | rms deviation from frequency-average (per time and pol) | | ||
| - | The correct scaling factors are applied in all cases. For "diff in freq" the difference between channels 0 and 1 is used for 0 etc, the last one is assigned zero. For "symmetric diff in freq" the first and last are assigned zero. | + | The correct scaling factors are applied in all cases. For "diff in freq" the difference between channels 0 and 1 is used for 0 etc, the last one is assigned zero. For "symmetric diff in freq" the first and last are assigned zero. The option "weights" is included for comparison, it defines the theoretical limit for perfect correlator efficiency and calibration (perfect coherence). |
| What we measure is the noise per time/frequency bin. This has to be translated to SEFD-like quantites per original sample by multiplying with sqrt (channel-width*integration-time). | What we measure is the noise per time/frequency bin. This has to be translated to SEFD-like quantites per original sample by multiplying with sqrt (channel-width*integration-time). | ||
| - | These procedures have different advantages and disadvantages. The "rms" is very simple, but only accurate if the calibration works perfectly, because otherwise residual calibration errors are misinterpreted as thermal noise. The differences are generally less affected by calibration problems. The more channels we have, the higher is the thermal noise relative to calibration residuals, so that the accuracy increases. | + | These procedures have different advantages and disadvantages. The "rms" is very simple, but only accurate if the calibration works perfectly, because otherwise residual calibration errors are misinterpreted as thermal noise. The option "rms2" works slightly better. The differences are generally less affected by calibration problems. The more channels we have, the higher is the thermal noise relative to calibration residuals, so that the accuracy increases. |
| From this we get several versions (real/imag for each of the 5 procedures) of noise-to-signal (N/S). If we multiply with the calibrator flux per channel, we obtain the SEFD for the baseline. To a very good approximation this is a factor of sqrt (2) smaller than the SEFD of individual stations (or the geometric mean of both SEFDs if they are different), as we will see below. | From this we get several versions (real/imag for each of the 5 procedures) of noise-to-signal (N/S). If we multiply with the calibrator flux per channel, we obtain the SEFD for the baseline. To a very good approximation this is a factor of sqrt (2) smaller than the SEFD of individual stations (or the geometric mean of both SEFDs if they are different), as we will see below. | ||
| Line 75: | Line 77: | ||
| {{:projects:mkat_sband:pub:snr_1sec.png?direct&400}} | {{:projects:mkat_sband:pub:snr_1sec.png?direct&400}} | ||
| - | Particularly in the 60-sec solution we find that the "rms" method does not work well. For 10-sec and 1-sec, everything gets closer together. In these cases the "diff in freq" and "symmetric diff in freq" methods are both very good and almost indistinguishable. For the future we will generaly use "symmetric diff in freq", unless noted otherwise. | + | Particularly in the 60-sec solution we find that the "rms" method does not work well. For 10-sec and 1-sec, everything gets closer together. In these cases the "diff in freq" and "symmetric diff in freq" methods are both very good and almost indistinguishable. For the future we will generaly use "symmetric diff in freq" with 1-sec solution intervals, unless noted otherwise. |
| - | Using the "symmetric diff in freq" result and combining the real and imaginary parts as mentioned, we can (under the assumption that both stations are equal) determine the SEFD+S and the SEFD from this baseline: \\ | + | Using the "symmetric diff in freq" result (and "weights" for comparison) and combining the real and imaginary parts as mentioned, we can (under the assumption that both stations are equal) determine the SEFD+S and the SEFD from this baseline. In the following plot we binned over 16 channels each: \\ |
| {{:projects:mkat_sband:pub:sefd_1sec.png?direct&500}} | {{:projects:mkat_sband:pub:sefd_1sec.png?direct&500}} | ||
| + | |||
| + | The SNR can be reduced or separated into station-based SNRs, as shown with the dashed yellow lines. These can hardly be distinguished from the solid (baseline-based) lines, which proves that the separation works well. | ||
