Main goal of this short branch is to discuss the concept for signal to noise ratio (SNR) measurement technique.
It is assumed that ELODIE includes 1959 spectra at three different resolutions:
| Resolution | Code |
|---|---|
| R=42000 | H |
| R=10000 | L |
| Blue fract. | Elo1 |
[Resolutions considered]
The previously stored data are now reloaded,
load(file = "/home/jb/git/pn2011/snr/elodie_res.RData")
The real SNR values have been provided as estimated from the array of sensors device.
After loading the different families of spectra, we calculate their SNR values as per element basis. Then we merged all the SNR estimations with the original one.
Our first estimation for the SNR was based only into the wavelength expression for the spectra with out taking care of any sub-spectra region.
We can depict some relationships depending on each data-set studied
plot(osnr[, 2], osnr[, 3], xlab = "Original SNR", ylab = "Measured SNR", main = "Relationship in case of Elo1 dataset")
plot(osnr[, 2], osnr[, 4], xlab = "Original SNR", ylab = "Measured SNR", main = "Relationship in case of L dataset")
plot(osnr[, 2], osnr[, 5], xlab = "Original SNR", ylab = "Measured SNR", main = "Relationship in case of H dataset")
The biggest conclusion is that it gets a wrong endpoint to associate a SNR value to a signal, to re-sample it and still considers this initial SNR as the good one.
In this way it is possible to realize how, for the biggest density (R=42000) there is a stronger relationship between some fraction of both spectra. Even when there is another set of spectra which are clearly uncorrelated.
osnr[1:20, ]
## THEORY D.SNR B.SNR L.SNR H.SNR
## 1 00001.fits 163.8 26.2394481246712 67.5230554616693 80.387641787958
## 2 00002.fits 288.8 361.398612567866 792.303514579114 269.266968402058
## 3 00003.fits 122.7 28.397618881473 62.1796934990082 74.5942053808666
## 4 00004.fits 137.3 30.4157467625289 71.2549576135147 80.8961004913999
## 5 00005.fits 101.1 12.8878536655673 23.9785331052851 27.052446993182
## 6 00006.fits 144.9 15.4119255615594 33.3450468407331 53.8588479708267
## 7 00007.fits 134.8 42.9762981206909 194.560573063463 109.360429963834
## 8 00008.fits 105.1 45.7922086863789 181.996115257925 89.2406366300405
## 9 00009.fits 80.7 45.1509638488004 152.633122795621 66.0652374631983
## 10 00010.fits 105.5 27.5296749602775 56.471982313251 63.8270265818283
## 11 00011.fits 120.9 17.0562902075109 32.7831945448975 47.0704185352661
## 12 00012.fits 73.6 56.7717060857951 126.725619462166 59.7811856481925
## 13 00013.fits 74.8 21.8103401437975 41.5268746926864 42.4882034728498
## 14 00014.fits 376.0 12.0862434983147 18.6512256856873 25.1858452094172
## 15 00015.fits 224.6 12.0041337176951 18.7040553824664 24.9494558706771
## 16 00016.fits 89.2 81.792193976718 232.658226130451 82.2784887816092
## 17 00017.fits 89.2 81.8429836737006 232.520209718436 82.2955728234692
## 18 00018.fits 187.2 22.4364059641126 48.3407376451479 70.6073725324837
## 19 00019.fits 72.1 17.8581165878733 36.554377031841 36.5030519194865
## 20 00020.fits 171.6 25.6097392978677 54.4687664192282 76.5534664675584
Now, it is time to have a look to the different periodograms at different sampling resolutions
Let us plot four plots per spectrum, which is its blue signal portion, its smoothed blue periodogram and then, periodograms for L and H resolutions.
for (i in 1:100) {
linea <- sprintf("%12s %10s %10s %10s %10s", osnr[i, 1], osnr[i, 2], osnr[i,
3], osnr[i, 4], osnr[i, 5])
par(mfrow = c(2, 2))
tit <- paste(rownames(rd_B[i, ]), " B fraction")
plot(1:length(rd_B[i, ]), rd_B[i, ], type = "l", main = tit, xlab = "Wavelength",
ylab = "Energy")
plot(sp_B[[i]], main = tit)
tit <- paste(rownames(rd_L[i, ]), " L fraction")
plot(sp_L[[i]], main = tit)
tit <- paste(rownames(rd_H[i, ]), " H fraction")
plot(sp_H[[i]], main = tit)
par(mfrow = c(1, 1))
cat("\n --------------------------------------------------------\n")
cat(paste("\n NAME ORIG_SNR BLUE_SNR L_SNR H_SNR\n",
linea, "\n", sep = ""))
}
##
## --------------------------------------------------------
##
## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00001.fits 163.8 26.2394481246712 67.5230554616693 80.387641787958
##
## --------------------------------------------------------
##
## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00002.fits 288.8 361.398612567866 792.303514579114 269.266968402058
##
## --------------------------------------------------------
##
## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00003.fits 122.7 28.397618881473 62.1796934990082 74.5942053808666
##
## --------------------------------------------------------
##
## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00004.fits 137.3 30.4157467625289 71.2549576135147 80.8961004913999
##
## --------------------------------------------------------
##
## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00005.fits 101.1 12.8878536655673 23.9785331052851 27.052446993182
##
## --------------------------------------------------------
##
## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00006.fits 144.9 15.4119255615594 33.3450468407331 53.8588479708267
##
## --------------------------------------------------------
##
## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00007.fits 134.8 42.9762981206909 194.560573063463 109.360429963834
##
## --------------------------------------------------------
##
## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00008.fits 105.1 45.7922086863789 181.996115257925 89.2406366300405
##
## --------------------------------------------------------
##
## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00009.fits 80.7 45.1509638488004 152.633122795621 66.0652374631983
##
## --------------------------------------------------------
##
## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00010.fits 105.5 27.5296749602775 56.471982313251 63.8270265818283
##
## --------------------------------------------------------
##
## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00011.fits 120.9 17.0562902075109 32.7831945448975 47.0704185352661
##
## --------------------------------------------------------
##
## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00012.fits 73.6 56.7717060857951 126.725619462166 59.7811856481925
##
## --------------------------------------------------------
##
## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00013.fits 74.8 21.8103401437975 41.5268746926864 42.4882034728498
##
## --------------------------------------------------------
##
## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00014.fits 376 12.0862434983147 18.6512256856873 25.1858452094172
##
## --------------------------------------------------------
##
## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00015.fits 224.6 12.0041337176951 18.7040553824664 24.9494558706771
##
## --------------------------------------------------------
##
## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00016.fits 89.2 81.792193976718 232.658226130451 82.2784887816092
##
## --------------------------------------------------------
##
## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00017.fits 89.2 81.8429836737006 232.520209718436 82.2955728234692
##
## --------------------------------------------------------
##
## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00018.fits 187.2 22.4364059641126 48.3407376451479 70.6073725324837
##
## --------------------------------------------------------
##
## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00019.fits 72.1 17.8581165878733 36.554377031841 36.5030519194865
##
## --------------------------------------------------------
##
## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00020.fits 171.6 25.6097392978677 54.4687664192282 76.5534664675584
##
## --------------------------------------------------------
##
## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00021.fits 146.3 13.6659834115573 19.3851077905171 18.8977286255618
##
## --------------------------------------------------------
##
## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00022.fits 122.3 13.6280067157854 25.9362051280911 32.4896315432305
##
## --------------------------------------------------------
##
## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00023.fits 120.8 168.430358872827 367.123008130785 139.593104439651
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## --------------------------------------------------------
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## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00024.fits 86 16.9139029912714 41.5892494523881 25.1143877202821
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## --------------------------------------------------------
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## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00025.fits 80.9 31.1164492290605 67.0562049363269 61.9031947053528
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## --------------------------------------------------------
##
## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00026.fits 131 17.5482807742963 35.1735868775017 51.7450889020917
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## --------------------------------------------------------
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## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00027.fits 131 17.891074353693 35.1289819054464 50.4301881201608
##
## --------------------------------------------------------
##
## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00028.fits 147.2 24.8024975046118 61.7336687413343 75.5853528235497
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## --------------------------------------------------------
##
## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00029.fits 365.5 23.2419251286493 63.3778038923205 98.4963218906934
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## --------------------------------------------------------
##
## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00030.fits 89 37.9320201273234 115.942673351236 71.2485887282714
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## --------------------------------------------------------
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## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00031.fits 138.4 14.7536416750242 27.738118392416 33.4642604763346
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## --------------------------------------------------------
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## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00032.fits 108.2 20.8386116138888 45.5338630992714 71.2744962611632
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## --------------------------------------------------------
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## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00033.fits 102.2 26.2134574466049 77.8132416460607 67.4542627026314
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## --------------------------------------------------------
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## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00034.fits 221.5 18.4110982521252 33.2968230728198 51.9581641550207
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## --------------------------------------------------------
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## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00035.fits 155.2 17.970586152863 33.5038013420126 46.847599873927
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## --------------------------------------------------------
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## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00036.fits 164.4 14.2634122885569 16.6243149293412 15.2260017445989
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## --------------------------------------------------------
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## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00037.fits 164.4 14.3015879228428 16.5780937307735 15.1644072481937
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## --------------------------------------------------------
##
## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00038.fits 153.2 17.8534172846971 35.669232556902 47.7453643976602
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## --------------------------------------------------------
##
## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00039.fits 198.4 20.2250031962217 38.9653874009591 61.9567626237417
##
## --------------------------------------------------------
##
## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00040.fits 306.8 16.2230524619354 17.9907016901975 16.2787973114162
##
## --------------------------------------------------------
##
## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00041.fits 142.4 14.4359143501906 28.2151598425204 35.3621739436809
##
## --------------------------------------------------------
##
## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00042.fits 76.6 22.2092651580072 44.0114482687244 40.9973535705084
##
## --------------------------------------------------------
##
## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00043.fits 268 14.2244117527958 29.6962009877559 40.0968866109588
##
## --------------------------------------------------------
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## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00044.fits 180 18.6025039980799 33.2333523028401 56.2083516470583
##
## --------------------------------------------------------
##
## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00045.fits 172.4 18.0815594965157 33.31581381656 55.1202353006186
##
## --------------------------------------------------------
##
## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00046.fits 504 15.7040488750347 33.41382679937 59.0577135438483
##
## --------------------------------------------------------
##
## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00047.fits 111.2 15.526850509764 30.1026209225429 32.7468506567652
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## --------------------------------------------------------
##
## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00048.fits 179.9 23.3778784444102 46.9827321968472 87.3271859090753
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## --------------------------------------------------------
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## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00049.fits 239.4 21.4075849409829 47.2939748308815 96.3398055268943
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## --------------------------------------------------------
##
## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00050.fits 163.4 20.644817613484 51.1105750585448 68.8622078103344
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## --------------------------------------------------------
##
## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00051.fits 216.4 23.138678429253 56.4103113668643 81.9000212372833
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## --------------------------------------------------------
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## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00052.fits 138.9 24.9991887352417 67.5198024951028 65.911964719044
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## --------------------------------------------------------
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## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00053.fits 187.6 79.4345170931581 277.891367867185 183.589025141535
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## --------------------------------------------------------
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## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00054.fits 143.8 59.5583642373229 228.403482216778 131.126295147672
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## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00055.fits 112.3 20.8965653827994 38.0657596875413 49.9557670636194
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## --------------------------------------------------------
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## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00056.fits 107.3 21.7110632294124 37.7592029659422 48.9818534866729
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## --------------------------------------------------------
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## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00057.fits 459 18.2157253500994 37.8501516908745 61.6826461628267
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## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00058.fits 337.7 20.9921175370521 38.1695839457817 64.623725295657
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## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00059.fits 103 15.1321735502605 31.6768332429989 38.2783481141006
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## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00060.fits 107.9 11.8957670646922 19.4205258409883 19.2235187321344
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## --------------------------------------------------------
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## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00061.fits 126.3 13.3645976145367 25.0988320602917 24.5902059161363
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## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00062.fits 135.4 400.495634937161 595.085881946495 146.34423420902
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## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00063.fits 133.9 431.007748990167 616.408119109531 144.070223859185
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## --------------------------------------------------------
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## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00064.fits 285.4 520.434653991229 796.248918480962 262.595833833026
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## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00065.fits 171.4 350.741749117086 546.200757646303 164.116886332725
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## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00066.fits 67.9 18.4449172955085 31.3978054830834 31.8591392035936
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## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00067.fits 77 16.5858655348958 31.7321826825624 33.2930099794468
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## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00068.fits 77 16.6797910923074 31.7161674948167 33.0422755371754
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## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00069.fits 158.6 18.7001052322045 17.4735640149576 15.2536358701554
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## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00070.fits 137.8 31.7151944149854 108.711242418234 137.584019834431
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## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00071.fits 165.8 30.5765692316526 106.882271665548 159.500106340467
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## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00072.fits 396.9 27.5546339348418 103.077744270606 219.735643193606
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## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00073.fits 106.1 13.3693984395335 28.6910113163917 35.223018508179
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## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00074.fits 168.5 13.3157597396552 27.0320682160936 36.8244487139704
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## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00075.fits 94.1 29.0294117623298 62.5032425908364 61.7738107387924
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## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00076.fits 193.2 41.4873682618799 151.083020958742 184.48357847065
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## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00077.fits 148.6 24.9541913700394 51.3140468285965 73.480583126725
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## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00078.fits 111.8 54.735381216308 138.276198806019 108.168395784496
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## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00079.fits 115.5 18.365958938163 33.669960867688 42.9140140347792
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## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00080.fits 184.7 20.8464093640226 38.2428331441551 62.0286670266411
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## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00081.fits 137.2 163.37822856365 365.818861390912 130.141648044385
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## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00082.fits 114.8 12.7769436598866 20.4778791545985 21.7282843828724
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## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
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## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
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## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
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## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
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## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
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## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
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## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
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## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
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## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00095.fits 148.3 23.9686463508869 48.9050690068165 72.0236074905422
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## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
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## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
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## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00098.fits 82.7 19.59268664785 47.7201884790249 41.072263148427
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## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00099.fits 274.4 628.725081168732 1232.65303268264 268.378568781598
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## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00100.fits 524.7 690.83104906538 1469.72168213026 350.199001460349
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## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00101.fits 183.6 564.366111957771 1003.94140709026 203.894046838163
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## NAME ORIG_SNR BLUE_SNR L_SNR H_SNR
## 00102.fits 177.5 492.752935651224 893.209106954764 196.414957698405
