#-> Title		Scattering matrix of the area expansion for a mean upstream Mach number of 0.05
#-> Date		2019-02-10
#-> Author 		Luck Peerlings, luck@kth.se
#				Marcus Wallenberg Laboratory of Sound and Vibration
#				Department of Aeronautical and Vehicle Engineering
#				School of Engineering Sciences
#				KTH Royal Institute of Technology
#-> Identifier
#
#-> MEASUREMENT SETUP
#	The measured scattering matrix is for an area expansion with an area expansion ratio of 0.3086.
#	The upstream duct has a radius of 25mm, The downstream duct has a radius of 45mm. The flow speed is based upon a uniform mean flow assumption with the same volume flow as that of the fully developed flow profile in the duct.	
#	See also "Assessing precision and accuracy in acoustic scattering matrix measurements", PhD Thesis, Luck Peerlings, KTH Royal Institute of Technology, URN: urn:nbn:se:kth:diva-206474
#
#-> MEASUREMENT CONDITIONS
#	Upstream flow speed M = 0.0469
#	Area-expansion ratio = 0.3086
#	Quasi-steady state scattering matrix = [-0.5524, 1.5517; 0.4789, 0.5213]
#
#->	README
#	The data is stored in tab delimited layout. The first row contains the indentifier for each column. Subsequent rows are the data obtained for various frequencies.
#	The first column gives the frequencies, denoted by "f".
#	The other columns containt the data of the elements of the scattering matrix. The indentifiers are given by "S¤¤", where ¤¤ is the position of the element in the matrix.
#	S11 is the upstream reflection coefficient, S21 is the downstream transmission coefficient, S12 is the upstream transmission coefficient and S22 is the downstream reflection coefficient.
#	"S¤¤_abs" gives the absolute value of the element, 
#	"S¤¤_angle" gives the angle in degrees of the element,
#	"S¤¤u_abs" gives the standard deviation of the absolute value and
#	"S¤¤u_angle" gives the standard deviation of the angle in degrees.
#	The standard deviation of the absolute value and phase are calculated using the approximation that the standard deviation in the real and imaginary part of the coefficient is much smaller than the absolute value of the coefficient. 
#	See also "In-Phase/Quadrature Covariance-Matrix Representation of the Uncertainty of Vectors and Complex Numbers" by D. F. Williams and C. M. Wang and U. Arz, National Institute of Standards and Technology.
#	Outliers in the data have not been removed.
#
#	This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by-sa/4.0/ or send a letter to Creative Commons, PO Box 1866, Mountain View, CA 94042, USA.
#
#->	START DATA
f	S11_abs	S11_angle	S11u_abs	S11u_angle	S12_abs	S12_angle	S12u_abs	S12u_angle	S21_abs	S21_angle	S21u_abs	S21u_angle	S22_abs	S22_angle	S22u_abs	S22u_angle
5.000000e+01	 6.919913e-01 	 -1.775129e+02 	 1.261139e-02 	 1.045750e+00	 1.619106e+00 	 1.176297e+00 	 2.162426e-02 	 7.358819e-01	 3.702393e-01 	 -9.276080e+00 	 1.108147e-02 	 1.768447e+00	 5.722989e-01 	 6.683564e+00 	 1.883011e-02 	 1.896476e+00
7.500000e+01	 5.422619e-01 	 -1.812745e+02 	 7.096358e-03 	 7.610295e-01	 1.541305e+00 	 -2.688134e-01 	 7.809237e-03 	 3.030704e-01	 4.862663e-01 	 8.049807e-01 	 5.544241e-03 	 6.511115e-01	 5.200153e-01 	 -2.709481e-01 	 5.885170e-03 	 7.095749e-01
1.000000e+02	 5.510401e-01 	 -1.815854e+02 	 4.517535e-03 	 4.674595e-01	 1.547905e+00 	 -7.102012e-01 	 7.076126e-03 	 2.615575e-01	 4.833538e-01 	 2.172199e-01 	 2.868023e-03 	 3.672191e-01	 5.260950e-01 	 1.415717e-01 	 4.166444e-03 	 5.759116e-01
1.250000e+02	 5.573929e-01 	 -1.807535e+02 	 4.097833e-03 	 4.353286e-01	 1.546972e+00 	 -3.775996e-01 	 6.497843e-03 	 2.573173e-01	 4.846663e-01 	 -3.287031e-01 	 1.990820e-03 	 2.978769e-01	 5.242447e-01 	 -2.294924e-02 	 2.423603e-03 	 4.435208e-01
1.500000e+02	 5.519542e-01 	 -1.807568e+02 	 4.995306e-03 	 5.734891e-01	 1.548425e+00 	 -7.590213e-01 	 1.021121e-02 	 5.428145e-01	 4.839038e-01 	 -1.198213e-01 	 2.084787e-03 	 2.981494e-01	 5.228361e-01 	 5.020444e-01 	 5.408067e-03 	 5.110896e-01
1.750000e+02	 5.572728e-01 	 -1.819538e+02 	 1.050031e-02 	 6.665699e-01	 1.556344e+00 	 -6.728517e-01 	 7.897580e-03 	 6.883329e-01	 4.863398e-01 	 -3.308364e-01 	 2.504045e-03 	 7.576028e-01	 5.199674e-01 	 -8.796781e-02 	 6.905682e-03 	 9.143637e-01
2.000000e+02	 5.586552e-01 	 -1.815131e+02 	 2.458778e-03 	 5.050164e-01	 1.551332e+00 	 -7.866995e-01 	 4.085215e-03 	 2.806494e-01	 4.842111e-01 	 -4.996494e-01 	 9.626977e-04 	 2.394419e-01	 5.182015e-01 	 4.168227e-01 	 1.660426e-03 	 4.363478e-01
2.250000e+02	 5.580367e-01 	 -1.820865e+02 	 5.098638e-03 	 3.657132e-01	 1.554557e+00 	 -8.920823e-01 	 5.691208e-03 	 2.933221e-01	 4.854484e-01 	 -5.340024e-01 	 2.177051e-03 	 2.864694e-01	 5.141323e-01 	 4.543064e-01 	 3.583663e-03 	 3.530347e-01
2.500000e+02	 5.583721e-01 	 -1.819133e+02 	 4.012406e-03 	 1.410171e+00	 1.567239e+00 	 -1.495663e+00 	 2.079778e-02 	 1.088232e+00	 4.857282e-01 	 -7.015298e-01 	 2.075099e-03 	 5.922574e-01	 5.121021e-01 	 9.621653e-01 	 9.132502e-03 	 8.798184e-01
2.750000e+02	 5.548483e-01 	 -1.825944e+02 	 1.007178e-02 	 9.834169e-01	 1.550570e+00 	 -1.634682e+00 	 1.360652e-02 	 1.050267e+00	 4.851803e-01 	 -7.692360e-01 	 1.819093e-03 	 6.473132e-01	 5.182905e-01 	 9.613680e-01 	 9.548251e-03 	 5.937465e-01
3.000000e+02	 5.594262e-01 	 -1.833469e+02 	 4.079080e-03 	 6.621382e-01	 1.554092e+00 	 -1.480392e+00 	 3.672087e-03 	 4.259649e-01	 4.851526e-01 	 -1.269754e+00 	 1.960714e-03 	 3.550851e-01	 5.147127e-01 	 6.309763e-01 	 2.929004e-03 	 5.304108e-01
3.250000e+02	 5.569028e-01 	 -1.837695e+02 	 4.718396e-03 	 7.532811e-01	 1.554677e+00 	 -1.563635e+00 	 2.630052e-03 	 4.660635e-01	 4.867644e-01 	 -1.333554e+00 	 1.695596e-03 	 3.921661e-01	 5.134447e-01 	 8.523104e-01 	 2.687104e-03 	 5.820943e-01
3.500000e+02	 5.619010e-01 	 -1.839586e+02 	 6.967532e-03 	 8.688283e-01	 1.554272e+00 	 -1.850913e+00 	 3.261857e-03 	 5.725069e-01	 4.841726e-01 	 -1.422324e+00 	 3.300099e-03 	 4.725730e-01	 5.149713e-01 	 7.308568e-01 	 1.923579e-03 	 7.507132e-01
3.750000e+02	 5.566801e-01 	 -1.846161e+02 	 7.883710e-03 	 5.266104e-01	 1.556045e+00 	 -2.155977e+00 	 9.301906e-03 	 6.162252e-01	 4.850883e-01 	 -1.630788e+00 	 2.059131e-03 	 4.605194e-01	 5.140702e-01 	 9.745744e-01 	 4.290423e-03 	 6.266706e-01
4.000000e+02	 5.650283e-01 	 -1.848246e+02 	 5.835353e-03 	 5.924952e-01	 1.548730e+00 	 -1.985458e+00 	 5.691115e-03 	 5.554868e-01	 4.832408e-01 	 -1.714747e+00 	 2.420120e-03 	 5.147413e-01	 5.173903e-01 	 1.014248e+00 	 3.850038e-03 	 7.809794e-01
4.250000e+02	 5.626006e-01 	 -1.850481e+02 	 1.745895e-03 	 8.191723e-01	 1.551671e+00 	 -2.167551e+00 	 5.300275e-03 	 6.468477e-01	 4.843696e-01 	 -1.715976e+00 	 1.070951e-03 	 5.481880e-01	 5.136838e-01 	 9.265668e-01 	 3.813245e-03 	 1.061886e+00
4.500000e+02	 5.179915e-01 	 -1.789359e+02 	 3.454006e-02 	 1.022185e+01	 1.518862e+00 	 -5.828396e+00 	 6.168916e-02 	 4.329125e+00	 4.337558e-01 	 1.371278e+00 	 6.516918e-02 	 4.324458e+00	 5.159842e-01 	 9.622019e+00 	 9.816775e-03 	 1.057024e+01
4.750000e+02	 5.626386e-01 	 -1.856742e+02 	 2.348870e-03 	 9.286308e-01	 1.550091e+00 	 -2.220019e+00 	 3.350234e-03 	 6.027343e-01	 4.843982e-01 	 -1.959033e+00 	 8.526853e-04 	 5.740614e-01	 5.161669e-01 	 1.312522e+00 	 2.350714e-03 	 1.198420e+00
5.000000e+02	 5.585646e-01 	 -1.868000e+02 	 1.293196e-02 	 1.865958e+00	 1.547561e+00 	 -2.454047e+00 	 2.030471e-02 	 8.014582e-01	 4.889967e-01 	 -1.479261e+00 	 1.128348e-02 	 1.632217e+00	 5.070116e-01 	 1.442667e+00 	 1.858674e-02 	 1.220433e+00
5.250000e+02	 5.562600e-01 	 -1.859515e+02 	 1.198048e-02 	 1.636002e+00	 1.565227e+00 	 -3.018066e+00 	 2.843707e-02 	 1.412972e+00	 4.832226e-01 	 -1.990244e+00 	 4.405021e-03 	 8.035381e-01	 5.090715e-01 	 2.184201e+00 	 1.153605e-02 	 1.319531e+00
5.500000e+02	 5.653614e-01 	 -1.868666e+02 	 1.052198e-02 	 6.941895e-01	 1.551376e+00 	 -2.596857e+00 	 5.743503e-03 	 6.892357e-01	 4.827929e-01 	 -2.166638e+00 	 4.990513e-03 	 6.354450e-01	 5.161170e-01 	 2.027434e+00 	 6.652029e-03 	 8.351171e-01
5.750000e+02	 5.587695e-01 	 -1.868569e+02 	 8.017698e-03 	 1.071135e+00	 1.552359e+00 	 -2.810276e+00 	 4.258435e-03 	 7.913074e-01	 4.855098e-01 	 -2.351701e+00 	 3.796098e-03 	 7.283610e-01	 5.113983e-01 	 1.961780e+00 	 3.267970e-03 	 1.166021e+00
6.000000e+02	 5.662355e-01 	 -1.867904e+02 	 9.617162e-03 	 1.824654e+00	 1.545478e+00 	 -3.214426e+00 	 1.261898e-02 	 1.288178e+00	 4.849808e-01 	 -2.253644e+00 	 1.763589e-03 	 8.431318e-01	 5.156947e-01 	 2.627916e+00 	 2.522013e-03 	 1.079391e+00
6.250000e+02	 5.628899e-01 	 -1.884732e+02 	 1.000352e-02 	 3.335719e+00	 1.552756e+00 	 -3.135690e+00 	 1.797245e-02 	 1.323737e+00	 4.812400e-01 	 -1.859275e+00 	 9.785018e-03 	 2.459137e+00	 5.212486e-01 	 2.060441e+00 	 1.600056e-02 	 1.840718e+00
6.500000e+02	 5.642547e-01 	 -1.874981e+02 	 3.517565e-03 	 1.460540e+00	 1.552259e+00 	 -3.076456e+00 	 5.967502e-03 	 8.154733e-01	 4.851363e-01 	 -2.620880e+00 	 1.251660e-03 	 6.973703e-01	 5.158565e-01 	 1.922772e+00 	 2.998609e-03 	 1.340799e+00
6.750000e+02	 5.760884e-01 	 -1.883698e+02 	 2.142909e-02 	 1.304595e+00	 1.544022e+00 	 -3.550034e+00 	 2.241820e-02 	 1.446661e+00	 4.856951e-01 	 -2.184872e+00 	 5.031629e-03 	 1.409959e+00	 5.130026e-01 	 2.886753e+00 	 1.278493e-02 	 1.474896e+00
7.000000e+02	 5.640614e-01 	 -1.879383e+02 	 1.599777e-02 	 1.693051e+00	 1.545689e+00 	 -3.658827e+00 	 1.535674e-02 	 1.561973e+00	 4.873140e-01 	 -2.536218e+00 	 6.907033e-03 	 1.159005e+00	 5.212897e-01 	 2.087266e+00 	 1.235339e-02 	 1.712869e+00
7.250000e+02	 5.721290e-01 	 -1.881905e+02 	 5.464575e-03 	 1.445315e+00	 1.552909e+00 	 -3.584994e+00 	 6.423727e-03 	 1.064094e+00	 4.850567e-01 	 -2.683772e+00 	 3.199141e-03 	 8.869061e-01	 5.182378e-01 	 2.188252e+00 	 2.425314e-03 	 1.498951e+00
7.500000e+02	 5.743482e-01 	 -1.896593e+02 	 8.177193e-03 	 1.979652e+00	 1.552579e+00 	 -3.718890e+00 	 1.186562e-02 	 1.097872e+00	 4.846532e-01 	 -2.376751e+00 	 5.865437e-03 	 1.846495e+00	 5.212660e-01 	 2.320603e+00 	 1.002834e-02 	 1.495313e+00
7.750000e+02	 5.693383e-01 	 -1.891466e+02 	 7.829304e-03 	 1.602960e+00	 1.551097e+00 	 -3.666440e+00 	 7.472660e-03 	 1.009219e+00	 4.872246e-01 	 -3.045641e+00 	 2.876070e-03 	 8.723455e-01	 5.171216e-01 	 2.467720e+00 	 3.208208e-03 	 1.858970e+00
8.000000e+02	 5.803094e-01 	 -1.890561e+02 	 2.623421e-02 	 2.614705e+00	 1.567038e+00 	 -4.304354e+00 	 3.575743e-02 	 1.795683e+00	 4.843558e-01 	 -2.525026e+00 	 1.368811e-02 	 1.683654e+00	 5.102593e-01 	 2.419076e+00 	 1.498639e-02 	 2.998191e+00
8.250000e+02	 5.632706e-01 	 -1.904238e+02 	 1.993398e-02 	 1.282209e+00	 1.564537e+00 	 -4.172598e+00 	 3.080185e-02 	 1.371370e+00	 4.870002e-01 	 -3.179383e+00 	 4.493526e-03 	 1.042045e+00	 5.146429e-01 	 3.735901e+00 	 7.326609e-03 	 1.540703e+00
8.500000e+02	 5.744253e-01 	 -1.907746e+02 	 1.077640e-02 	 1.597417e+00	 1.541149e+00 	 -4.417102e+00 	 2.577393e-02 	 1.243519e+00	 4.884180e-01 	 -3.504701e+00 	 3.211876e-03 	 9.045887e-01	 5.229977e-01 	 3.195406e+00 	 1.201288e-02 	 1.359195e+00
8.750000e+02	 5.669673e-01 	 -1.912775e+02 	 8.509184e-03 	 1.680102e+00	 1.544445e+00 	 -4.491451e+00 	 1.404256e-02 	 1.474327e+00	 4.894432e-01 	 -3.326792e+00 	 4.306302e-03 	 1.365357e+00	 5.206353e-01 	 2.482529e+00 	 6.367370e-03 	 2.638160e+00
9.000000e+02	 5.693305e-01 	 -1.918282e+02 	 3.456911e-03 	 1.562277e+00	 1.554051e+00 	 -4.579813e+00 	 3.951583e-03 	 1.336575e+00	 4.887382e-01 	 -3.739303e+00 	 2.137440e-03 	 1.136858e+00	 5.153709e-01 	 2.917333e+00 	 4.947616e-03 	 2.316999e+00
9.250000e+02	 5.712157e-01 	 -1.919378e+02 	 7.818532e-03 	 2.076726e+00	 1.565143e+00 	 -4.925036e+00 	 2.824761e-02 	 1.488885e+00	 4.870159e-01 	 -3.886893e+00 	 4.713557e-03 	 1.228218e+00	 5.097548e-01 	 3.016744e+00 	 1.396450e-02 	 2.176299e+00
9.500000e+02	 5.658989e-01 	 -1.931980e+02 	 1.106583e-02 	 1.194328e+00	 1.559909e+00 	 -5.218265e+00 	 1.887376e-02 	 1.484299e+00	 4.872075e-01 	 -4.064638e+00 	 2.612661e-03 	 1.066449e+00	 5.152522e-01 	 4.566104e+00 	 6.559539e-03 	 1.906504e+00
9.750000e+02	 5.753017e-01 	 -1.929717e+02 	 8.078990e-03 	 1.749365e+00	 1.537607e+00 	 -5.145767e+00 	 2.763815e-02 	 1.263943e+00	 4.884449e-01 	 -4.420687e+00 	 2.853050e-03 	 1.133731e+00	 5.239779e-01 	 3.311746e+00 	 1.481891e-02 	 1.676187e+00
1.000000e+03	 5.721924e-01 	 -1.937806e+02 	 3.399678e-03 	 1.495121e+00	 1.547295e+00 	 -5.232664e+00 	 9.260090e-03 	 1.637619e+00	 4.865861e-01 	 -4.108821e+00 	 1.213457e-03 	 2.004857e+00	 5.209816e-01 	 2.975113e+00 	 9.547265e-03 	 3.097149e+00
1.025000e+03	 5.733004e-01 	 -1.938481e+02 	 2.359016e-03 	 1.489315e+00	 1.552560e+00 	 -5.352760e+00 	 9.120983e-03 	 1.416549e+00	 4.862276e-01 	 -4.685049e+00 	 1.061245e-03 	 1.266310e+00	 5.155099e-01 	 3.229684e+00 	 6.022714e-03 	 2.689004e+00
1.050000e+03	 5.728930e-01 	 -1.943447e+02 	 4.135040e-03 	 1.392258e+00	 1.554399e+00 	 -5.840483e+00 	 1.762776e-02 	 1.652937e+00	 4.859546e-01 	 -4.713271e+00 	 1.332801e-03 	 1.309658e+00	 5.112637e-01 	 4.313301e+00 	 1.246666e-02 	 1.866159e+00
1.075000e+03	 5.757585e-01 	 -1.947259e+02 	 5.579360e-03 	 1.472371e+00	 1.543068e+00 	 -5.765368e+00 	 7.090904e-03 	 1.599946e+00	 4.840308e-01 	 -4.699272e+00 	 2.926054e-03 	 1.389136e+00	 5.207777e-01 	 4.078089e+00 	 7.638593e-03 	 2.309406e+00
1.100000e+03	 5.714885e-01 	 -1.950253e+02 	 7.964256e-03 	 1.813878e+00	 1.551089e+00 	 -5.904006e+00 	 1.922323e-02 	 1.630438e+00	 4.843543e-01 	 -5.075904e+00 	 2.429957e-03 	 1.303167e+00	 5.136414e-01 	 4.393097e+00 	 1.119409e-02 	 2.065142e+00
1.125000e+03	 5.755990e-01 	 -1.954384e+02 	 1.178769e-02 	 1.682564e+00	 1.531510e+00 	 -6.157127e+00 	 2.568963e-02 	 1.887515e+00	 4.887702e-01 	 -5.253456e+00 	 1.705732e-02 	 1.434427e+00	 5.282124e-01 	 4.849921e+00 	 1.553269e-02 	 2.816182e+00
1.150000e+03	 5.712137e-01 	 -1.957517e+02 	 8.707472e-03 	 2.165923e+00	 1.533306e+00 	 -5.710587e+00 	 1.791681e-02 	 1.670067e+00	 4.841050e-01 	 -5.250848e+00 	 4.790708e-03 	 1.556534e+00	 5.245048e-01 	 4.258315e+00 	 9.461492e-03 	 3.452104e+00
1.175000e+03	 5.709893e-01 	 -1.960519e+02 	 2.557851e-03 	 2.254283e+00	 1.542879e+00 	 -6.018013e+00 	 9.270429e-03 	 1.725764e+00	 4.822551e-01 	 -5.227764e+00 	 1.507070e-03 	 1.326732e+00	 5.186214e-01 	 3.964823e+00 	 4.296800e-03 	 2.952183e+00
1.200000e+03	 5.690353e-01 	 -1.964766e+02 	 4.750952e-03 	 2.218301e+00	 1.549501e+00 	 -6.234958e+00 	 3.778963e-02 	 2.023585e+00	 4.830177e-01 	 -5.018744e+00 	 2.367301e-03 	 2.226551e+00	 5.084736e-01 	 4.754098e+00 	 2.632497e-02 	 2.091136e+00
1.225000e+03	 5.652753e-01 	 -1.967932e+02 	 7.942997e-03 	 1.997666e+00	 1.540732e+00 	 -7.391687e+00 	 1.372888e-02 	 3.196707e+00	 4.811872e-01 	 -5.354624e+00 	 2.882049e-03 	 1.594594e+00	 5.262879e-01 	 7.144871e+00 	 7.812250e-03 	 3.728829e+00
1.250000e+03	 5.700965e-01 	 -1.965087e+02 	 5.710763e-03 	 2.106931e+00	 1.518145e+00 	 -6.121056e+00 	 3.416031e-02 	 1.729022e+00	 4.855215e-01 	 -5.637616e+00 	 9.422349e-03 	 1.435525e+00	 5.316692e-01 	 4.432174e+00 	 1.954830e-02 	 2.457521e+00
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2.250000e+03	 5.779892e-01 	 -2.076526e+02 	 2.667392e-03 	 3.305766e+00	 6.457990e-01 	 1.070502e+02 	 1.474139e-02 	 3.027271e+00	 1.341320e-01 	 -8.929308e+01 	 2.743685e-03 	 5.655347e+00	 1.224418e+00 	 1.360930e+02 	 8.286748e-03 	 3.071696e+00
2.275000e+03	 5.356896e-01 	 -2.182351e+02 	 4.915753e-03 	 3.586993e+00	 1.200704e+00 	 4.640909e+01 	 1.247604e-02 	 2.653647e+00	 1.931846e-01 	 -1.246526e+01 	 6.821728e-03 	 5.874216e+00	 1.035202e+00 	 7.585603e+01 	 1.201492e-02 	 3.723112e+00
2.300000e+03	 6.075958e-01 	 -2.058086e+02 	 3.487869e-03 	 3.689750e+00	 4.912634e-01 	 -1.303384e+02 	 1.034922e-02 	 4.281727e+00	 1.315609e-01 	 -7.274805e+01 	 5.176783e-03 	 5.281439e+00	 1.135756e+00 	 1.926584e+02 	 8.836513e-03 	 3.271390e+00
#END DATA