1 / 50

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.

anthea
Download Presentation

Fourier Synthesis

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related