Hello everyone. I am trying to use the Shannon sampling to find an analytic expression for some 2D data as defined in this article.
My data is a 10*10 square with values at (1,1), (1,2), ...(10, 10). If I do it directly, the original data is reconstructed reasonably well. However, if I do a regular interpolaton and then I use the sampling over the obtained function, the results look nothing at all like the original ones. I am doing this as a test to see if I can find an alaytic expression for a dataset with a higher number of values; however, if even using the same number of points coming from the interpolation instead of the original dataset provide with a very different result, does it mean that I can't use this to find out an analytic expression for my original data?.
All my used files are attached to the code in case you want to take a look.
If anyone could tell me why my Shannon interpolation of the original data looks so different from the Shanon interpolation of the regularly interpolated I would be very thankful.
Regards. Jaime.
Note: It looks like the data file cannot be uploaded, so these are the values that I am using as f(x,y) in p8.dat:
1.2350100549134866 1.1044131456029633 0.8252143796872555 0.41301054910385915 -0.10836892884213323 -0.7082659375818571 -1.3510077983552655 -1.9980283698411245 -2.610174591721433 -3.150065272778294 -3.584364557896828 -3.885835812521737 -4.035052595583356 -4.02166150191382 -3.845116092291889 -3.514830673126462 -3.0497357986118536 -2.477252256998665 -1.8317350191029582 -1.1524711615088292 -0.48134417104996735 0.13970050030712816 0.6712387427574124 1.0788436282775988 1.3353002512341565 1.4224182143634947 1.332321531415459 1.0681248069677234 0.6439400882837389 0.08419878794706553 -0.5776847820904113 -1.301240000774928 -2.0413497118392523 -2.751003148270776 -3.384226743889595 -3.8990120607990244 -4.260055581797635 -4.441132307464469 -4.426943868696732 -4.21431137194261 -3.8126218623109227 -3.2434828926377146 -2.539589468608815 -1.7428584799134623 -0.9019343334427434 -0.06921262858568267 0.7024366289352144 1.363041103591947 1.8687774911089532 2.1848892197511356 2.2880746638164586 2.1681804351444383 1.8290763021382215 1.288639349413987 0.5778319500210065 -0.26108268520076267 -1.1770860917724253 -2.1135580052148684 -3.0118415933537213 -3.8149937583116507 -4.471477691688037 -4.938554637953677 -5.18514779201505 -5.193982654882354 -4.962853161325655 -4.504918681685028 -3.848000007180584 -3.032908519647427 -2.110907506790098 -1.140463614175696 -0.18349564659587958 0.6986361285997827 1.4491369830190073 2.0195152688354634 2.372800030560517 2.4860205591718163 2.3517771542023675 1.9787917531605856 1.3913945729381172 0.6279739771969208 -0.2615133648225991 -1.218811097130535 -2.1811961674295466 -3.085622431295128 -3.8728986802575838 -4.491621050417818 -4.901594888938527 -5.076514345992138 -5.005717066735738 -4.694893120574216 -4.165697572072553 -3.4542901093984266 -2.6088978592072127 -1.686563953025538 -0.7493000004245819 0.14009847294304756 0.922291194205585 1.5454003014233004 1.968514198000843 2.1644506402178068
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