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Fourier Synthesis

Fourier Synthesis. Sinusoidal Functions as “Building Blocks” for Spatial Vision. “Sinusoidal Function ” F(  ) = sin(  ). . sin(  ). sin( 0 ) = 0.0. sin( 45 ) = 0.7. sin(9 0 ) = 1.0. sin( 135 ) = 0.7. sin(18 0 ) = 0.0. sin( 225 ) = - 0.7. sin(27 0 ) = - 1.0. sin( 315 ) = - 0.7.

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Fourier Synthesis

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  1. Fourier Synthesis Sinusoidal Functions as “Building Blocks”for Spatial Vision

  2. “Sinusoidal Function” F() = sin()  sin()

  3. sin(0) = 0.0

  4. sin(45) = 0.7

  5. sin(90) = 1.0

  6. sin(135) = 0.7

  7. sin(180) = 0.0

  8. sin(225) = -0.7

  9. sin(270) = -1.0

  10. sin(315) = -0.7

  11. sin(360) = sin(0) = 0.0

  12. sin() F(x) = sin(x)

  13. F(x) = sin(x)

  14. F(x) = sin(x)

  15. F(x) = sin(x)

  16. F(x) = sin(x)

  17. F(x) = square(x)

  18. Two-dimensional F(x,y) Vertical position (y) Horizontal position (x)

  19. Two-dimensional F(x,y) Vertical position (y) Horizontal position (x)

  20. F(x,y) = one of an infinite functions of (x,y)

  21. One-dimensional F(x) = square(x)

  22. F(x) = square(x)  sin(x)

  23. F(x) = square(x)  sin(x)

  24. F(x) = sin(x)+1/3 sin(3x)

  25. F(x) = sin(x)+1/3 sin(3x) +1/5 sin(5x)

  26. F(x) = sin(x)+1/3 sin(3x) +1/5 sin(5x) +1/7 sin(7x)

  27. F(x) = sin(x)+1/3 sin(3x) +1/5 sin(5x) +1/7 sin(7x) +1/9 sin(9x)

  28. F(x) = sin(x)+1/3 sin(3x) +1/5 sin(5x) +1/7 sin(7x) +1/9 sin(9x) +1/11 sin(11x)

  29. F(x) = sin(x)+ 1/3 sin(3x) + 1/5 sin(5x) + 1/7 sin(7x) + 1/9 sin(9x) + 1/11 sin(11x) + 1/13 sin(13x)

  30. F(x) = sin(x)+1/3 sin(3x) +1/5 sin(5x) +1/7 sin(7x) + 1/9 sin(9x) + …...+1/25 sin(25x)

  31. F(x) = 1sin(1x)+1/3 sin(3x) +1/5 sin(5x) +1/7 sin(7x) + 1/9 sin(9x) + …...+1/25 sin(25x) [freq components]

  32. F() = (1 ,1)+(1/3 ,3) +(1/5 ,5) + (1/7 ,7) + (1/9,9) + …...

  33. F() = 1, 0, 1/3, 0, 1/5 , 0, 1/7 , 0, 1/9, …... “Frequency domain” “Spatial domain”

  34. Fourier Pairs

  35. Fourier Pairs

  36. Fourier Pairs

  37. Fourier Pairs

  38. Fourier Pairs

  39. Fourier Pairs

  40. Fourier Pairs

  41. Fourier Pairs

  42. Fourier Pairs

  43. Low-pass Filtering

  44. High-pass Filtering

  45. Frequency Channels

  46. 2D Gabor Functions

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