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# Untitled

a guest Jun 25th, 2019 59 Never
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1. %Basis vectors with coefficients:
2. f = @(x, y,a1,a2,a3,a4,b1,b2,b3,b4,c1,c2,c3,c4,d1,d2,d3,d4)...
3. a1*cos(0*x + 0*y) + a2*cos(0*x + 1*y) +...
4. a3*cos(0*x + 2*y) + a4*cos(0*x + 3*y) + ...
5. b1*cos(1*x + 0*y) + b2*cos(1*x + 1*y) + ...
6. b3*cos(1*x + 2*y) + b4*cos(1*x + 3*y) + ...
7. c1*cos(2*x + 1*y) + c2*cos(2*x + 1*y) + ...
8. c3*cos(2*x + 2*y) + c4*cos(3*x + 3*y) + ...
9. d1*cos(3*x + 1*y) + d2*cos(3*x + 1*y) + ...
10. d3*cos(3*x + 2*y) + d4*cos(3*x + 3*y)
11. %Matrix of image space:
12. [X,Y] = meshgrid(0:3);
13. %Creating the image from Fourier space by assigning coefficients:
14. F = f(X,Y,1,1,-1,1,1,1,1,6,3,1,1,1,7,1,1,1)
15.
16. F =
17.
18.    27.00000   -6.10793    5.54833  -12.13151
19.    -0.17799  -11.46000    6.76692    3.21717
20.     3.50819    6.10159    4.59486   -5.21914
21.   -18.13973    3.19193   -7.90075    6.77199
22.
23.
24. Fourier =
25.
26.     5.5639 +  0.0000i    3.1811 +  0.9129i   36.8357 +  0.0000i    3.1811 -  0.9129i
27.     5.3234 - 14.4227i   33.6355 +  2.0031i   43.5672 - 50.8361i   11.4412 -  8.5912i
28.    41.0249 +  0.0000i   37.5489 - 35.6015i   79.1810 +  0.0000i   37.5489 + 35.6015i
29.     5.3234 + 14.4227i   11.4412 +  8.5912i   43.5672 + 50.8361i   33.6355 -  2.0031i
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