How is this array of floats encoded?

Question

I am trying to decode an array of data from a piece of legacy equipment in to a more useful format.

I have the following base64 encoded string:
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When adding trailing padding and decoding this from base64, it produces an unknown binary format.

What I know so far based on limited inspection of the application:

• It is definitely base64.
• This array describes a series of floating point data (with values between 19 and 50) that consists of 201 points.
• The application that created this was likely written in .NET.

How is this data encoded, and can you provide psuedo-code to decode it?

Update #1:

• This data describes a return loss measurement waveform from an old network analyser.
• The expected values above are based on what the instrument displays, and it is possible that they are calculated from real and imaginary components.

Update #2: I've found there was also a CSV version of the data for this series. Expected values are:

28.6740250379346, 26.031723427971, 26.6849726930916, 27.5095233036572, 27.9755283611409, 28.0419902829292, 27.9918713318024, 28.0331481409078, 28.2620361924923, 29.1899991143532, 30.4746778667205, 31.9841888600965, 32.7562027026775, 32.2032446202011, 31.0251062040461, 30.1158617686259, 29.5968352710132, 29.8991302542384, 30.7711739051407, 32.5985879649759, 35.465787543584, 38.4033014264434, 36.2400347268325, 33.230539516557, 30.816214031517, 29.493776099706, 28.9641221620517, 29.3271399473768, 30.5497479471498, 32.9092924040263, 36.23602780908, 36.6766990656565, 32.9072309537322, 29.8008349575816, 27.8506153462939, 26.8255601987161, 26.7773337706284, 27.6450826739213, 29.6698279365727, 32.925219461411, 34.9915552473819, 31.6841927998324, 28.219566759529, 25.990640197895, 24.8525028738483, 24.6159871249645, 25.2752655673475, 26.9870507463537, 29.9877735491643, 33.2675296198038, 31.6015986278861, 27.8240493530138, 25.2742229688217, 23.9448603205908, 23.5140204346426, 23.9914986842046, 25.5009034820686, 28.1555920133881, 31.3075467263927, 30.7066273219751, 27.2707536503799, 24.7348022011574, 23.2637028240862, 22.7794008043094, 23.1669728824416, 24.5474786226331, 26.9949958437379, 30.2488348819328, 30.6013906923573, 27.3394012893084, 24.6326441335966, 23.0411076555662, 22.4181795795548, 22.7062561945124, 23.8692711954611, 26.163804153602, 29.606819207681, 31.2543679681834, 28.1493119289191, 25.0924674969376, 23.2520785937701, 22.4092737645517, 22.5015858777069, 23.4763598655373, 25.5208843109912, 28.9618678298617, 32.6403317308031, 30.3536019856501, 26.5991532707429, 24.2773569962831, 23.1127901052235, 22.9043583677862, 23.6093457155953, 25.3499073692444, 28.4637157202952, 32.8016120624956, 32.4896370664701, 28.3239184297021, 25.5279166849078, 24.0185490655501, 23.5330605365427, 23.8948677486768, 25.2054578354006, 27.7143031565687, 31.5869657438201, 33.7333955992785, 30.3948949895062, 27.1037601765126, 25.2161101159979, 24.3558529725873, 24.3231491126384, 25.2139427454679, 27.1233066134797, 30.3453761997478, 34.4047437237606, 33.8064220094595, 29.9215033359328, 27.3307978071688, 25.8801149514006, 25.4718657467003, 25.8501031953971, 27.1888665858689, 29.5756748124031, 32.9812339884177, 35.3068159226901, 32.6414213429246, 29.5799546795568, 27.7291120251878, 26.9050286745762, 26.9075167887431, 27.7591889971496, 29.3670540494547, 31.7578198149182, 33.5065256564295, 32.6776622084245, 30.4203840091006, 28.688025867147, 27.7417192975661, 27.4916484304414, 27.9791419175041, 29.2902681126682, 31.4107407957172, 33.4602036884894, 33.9200015192937, 32.1201008630103, 30.1453133278815, 28.7841082718969, 28.136959973426, 28.109171467367, 28.8259362791248, 30.0289196496445, 31.326134345957, 32.0708833202456, 31.4950426416152, 30.1423739250155, 29.0036769811377, 28.2190253962644, 28.1086422581195, 28.4750473325836, 29.1942813484775, 29.7608412256926, 29.6876433997282, 28.689538924267, 27.2407586615062, 26.0067421520125, 25.1638342823008, 24.8250524294419, 24.9395261449731, 25.4584143514754, 25.8777584307235, 25.6465050536004, 24.5707670056442, 23.0511544464452, 21.7615681906835, 20.9761497089273, 20.7854547053249, 21.2816973223554, 22.253260423558, 23.2052378948627, 23.4706372938485, 23.2944515491774, 23.1680235174658, 23.5290621578115, 24.4333231530622, 25.8639616096787, 27.9401749621508, 30.7364242326027, 33.9420488375473, 35.6377896682262, 33.4869702934454, 30.5820901568128, 28.3404467791117, 26.8270077060156, 26.0018669972732, 25.9446717292131, 26.5828002183748, 28.0360464264943, 30.0958735279379, 31.2921110009257, 29.5253906387702, 26.6971475290807

Answer 1

To advance the cause,

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

Converts to hex dump

89618bbe 052317bd ffb56d3e 100643bd ff9c623e a93f0fbd 60b1633e a6029dbc e0be6e3e 044615bc 1bce7c3e 10b418bc cdd4823e 523b96bc e0ab823e 1d86f5bc cba97d3e 6c6f19bd 898c723e 1dc918bd c8206b3e a278fabc 19e1693e b241adbc 52b36e3e 2d355ebc 76da763e 3d932fbc c8b67e3e 64265bbc fe5f813e b755a3bc 13eb803e 0638dfbc bd527c3e 78e502bd 8b5f753e 265704bd 13b36f3e b3f7e7bc a9e86d3e 306fb2bc ccea703e 51f283bc 4631763e 2ac550bc 79d77c3e c4745ebc cfef803e a54796bc 6b4f813e 901bcebc 3db57e3e 7061ffbc 22d2773e 866b08bd 6105713e fd52fcbc 5e4c6d3e 6125c9bc 4d736e3e 2d458dbc 8f44743e 6ac545bc 30937c3e a6b53fbc 1ab2813e 082189bc 4bc8823e cf5dcdbc a7da803e e08408bd d349793e db5318bd f9e86f3e f1230fbd 0c486a3e 5eb1dfbc 27f36a3e e82391bc e3fc713e a6bd2cbc 63a67c3e 4ae818bc a4fa823e 73987bbc 88a5843e b62bd8bc c23b823e f12818bd 8a92793e ee282ebd 4cb96d3e 637f23bd d860663e 5c70fabc 85da663e 9f1498bc d4246f3e 20e720bc 2cd87b3e 72630abc 2c52833e 998080bc 70fc843e a6cbeabc 23da813e 96d126bd aae8763e e3973cbd 276d693e 09492cbd d4c6613e fb49fabc 8c87633e 47b28bbc 20df6d3e 3728fcbb 28487c3e 3cb4eabb daf1833e b88885bc e837853e 5507fdbc c44d813e 547b33bd 5807743e d52f47bd e9bd653e ae4c31bd 40615e3e eb26f8bc 8319613e a5cf82bc 54b86c3e 1b86d8bb ab087c3e 9a2fe0bb e2da833e 45578cbc d5c5843e 2c7505bd 5542803e b59e3abd bb3e713e c5d34bbd 0eda623e 30f331bd d0d55b3e 4072f6bc 8e245f3e 8b377dbc 87466b3e abadd1bb 2ea77a3e f984e9bb 57f8823e 2d328fbc 5ec1833e 06ab06bd 7b7f7e3e f04b3abd 746d6f3e ddf94abd 966a613e 6bc331bd 677d5a3e bca9f8bc 5a675d3e b30f85bc 67b6683e a464efbb b022773e 85b9f9bb 82fa803e c60c8bbc 3fea813e b542febc bedb7b3e 9c382fbd d8186e3e 137f3fbd ef02613e af7029bd 4c6f5a3e 0fabf1bc a7d55c3e 806585bc eb06673e 707100bc 777a743e 3b88f7bb beb37e3e 05ec80bc b88a803e dedae8bc d53d7a3e 201922bd 00e56d3e cc6c33bd 46af613e f46d21bd f2e85a3e e809ecbc 58495c3e fa5e88bc 2332653e c54e00bc d69c713e 81ead5bb 73057c3e ded255bc 0a8e7f3e 4beac8bc 84bd7a3e 55c811bd 0e19703e d68927bd 5f66643e 0ebc1dbd 72b85c3e 4e69f4bc 213c5c3e bfd797bc c0d3623e b7d81bbc b1996d3e ea9ad1bb 22e7773e a51d2bbc 71f37c3e 9ddda1bc c8c97a3e 7ab3f5bc 8a78723e 1ea114bd 8419683e 993614bd 4b30603e ba3ff2bc 4f025e3e 299da3bc 7169623e 6c1935bc f46b6b3e 93e8d7bb 532c753e 16d908bc d5747b3e f68281bc 07857b3e 843dcebc d9a6753e 79f503bd 97826c3e 0f360bbd 9b6f643e 74f4f3bc 4bb6603e 9e3bb0bc e40f633e 892351bc 44536a3e d6f1e8bb 0ec8733e e2b7e6bb 1a6c7b3e a3c04dbc 13ca7d3e e497afbc 0d377a3e f4a9f3bc bd49723e 71260bbd d381693e cf3905bd 7e85633e fc4ed8bc 5b90623e af3d92bc e533673e 184f2ebc 595a6f3e 4148febb b0b3773e 872324bc 1eb27c3e e7a489bc 8b647c3e 6ae1cebc 77e2763e 1d4401bd c8956e3e a61208bd f408673e 349ff2bc 1927633e ee08b7bc 64c4643e e01165bc ff356b3e 427e04bc ddec733e e437e4bb 40e07b3e 165039bc 36977f3e 05e59ebc 9ba67d3e 8d41e6bc 9a95763e 004a0abd bb6c6d3e 10130cbd e6ec653e 6f65ebbc e258633e 547ba3bc e2d6663e 363035bc 72a16f3e b5b9b4bb ecaa7a3e 1393d4bb 1da5813e 27cc68bc f0cb823e 9dbdd4bc 2eab7f3e 154c18bd d783733e 1ff22ebd a5f3653e 98f221bd 16f05c3e 5099e8bc a6255d3e 6a955cbc 4881673e ff146dba f71b793e 2b61313b f448853e f880dbbb 2000893e 769fdbbc 9644843e fa1445bd 8502713e 09926bbd 7489583e bb3243bd 9f6d4e3e 6052bbbc 7ae2593e 577de73a f83e743e b4aa293c 86c6853e 0ffb0bbb 15b4883e 331bcfbc 9d37833e 57ac30bd fc51753e b6a844bd 63d4673e 6bd62dbd 9a93613e b06804bd 6634623e f3a8b6bc 7a7f673e 3ff17abc 85e86e3e 447247bc a95b763e f16356bc d37d7c3e 97298fbc 91817f3e 3f2ec8bc bb3b7e3e 226904bd c471783e 9c561ebd dbb56f3e 0f7c27bd 2abe663e 8d2e19bd 8d5d613e 869fefbc f010623e f4c59abc c47a693e 25902cbc 1773753e c47f08bc d677803e 90756bbc 2b46833e 6fe6dabc

402 32-bits.

Or more nicely formatted and re-endian-ized.
Looks like values are encoded as IEEE 32-bit float scaled up by about 122 or some magic number - depending on which values first expected value is 28.62 and the last is 31.32 map to.

  0 BE8B6189 BD172305 -0.272229  -0.036899*
  1 3E6DB5FF BD430610  0.232140* -0.047613
  2 3E629CFF BD0F3FA9  0.221302  -0.034973
  3 3E63B160 BC9D02A6  0.222356  -0.019166
  4 3E6EBEE0 BC154604  0.233150  -0.009111
  5 3E7CCE1B BC18B410  0.246880  -0.009320
  6 3E82D4CD BC963B52  0.255530  -0.018339
  7 3E82ABE0 BCF5861D  0.255218  -0.029971
  8 3E7DA9CB BD196F6C  0.247718  -0.037460
  9 3E728C89 BD18C91D  0.236864  -0.037301
 10 3E6B20C8 BCFA78A2  0.229617  -0.030575
...
195 3E615D8D BCEF9F86  0.220083  -0.029251
196 3E6210F0 BC9AC5F4  0.220768  -0.018893
197 3E697AC4 BC2C9025  0.228007  -0.010532
198 3E757317 BC087FC4  0.239697  -0.008331
199 3E8077D6 BC6B7590  0.250914  -0.014371*
200 3E83462B BCDAE66F  0.256395* -0.026721

... it is possible that they are calculated from real and imaginary components.

Note, with ignoring the first data value:
last complex pair magnitude / first complex pair magnitude
|-0.014371 + 0.256395 * i| / | -0.036899 + 0.232140 * i| is 1.093...

Much like 31.32/28.62 is 1.094...