# © 2000 Jeff B. Pelz. Fourier Synthesis Sinusoidal Functions as Building Blocks for Spatial Vision.

## Presentation on theme: "© 2000 Jeff B. Pelz. Fourier Synthesis Sinusoidal Functions as Building Blocks for Spatial Vision."— Presentation transcript:

Fourier Synthesis Sinusoidal Functions as Building Blocks for Spatial Vision

© 2000 Jeff B. Pelz Sinusoidal Function F( ) = sin( ) sin( )

© 2000 Jeff B. Pelz sin(0) = 0.0

© 2000 Jeff B. Pelz sin(45) = 0.7

© 2000 Jeff B. Pelz sin(90) = 1.0

© 2000 Jeff B. Pelz sin(135) = 0.7

© 2000 Jeff B. Pelz sin(180) = 0.0

© 2000 Jeff B. Pelz sin(225) = - 0.7

© 2000 Jeff B. Pelz sin(270) = - 1.0

© 2000 Jeff B. Pelz sin(315) = - 0.7

© 2000 Jeff B. Pelz sin(360) = sin(0) = 0.0

© 2000 Jeff B. Pelz F(x) = sin(x) sin( )

© 2000 Jeff B. Pelz F(x) = sin(x)

© 2000 Jeff B. Pelz F(x) = sin(x)

© 2000 Jeff B. Pelz F(x) = sin(x)

© 2000 Jeff B. Pelz F(x) = sin(x)

© 2000 Jeff B. Pelz F(x) = square(x)

© 2000 Jeff B. Pelz Two-dimensional F(x,y) Horizontal position (x) Vertical position (y)

© 2000 Jeff B. Pelz Two-dimensional F(x,y) Horizontal position (x) Vertical position (y)

© 2000 Jeff B. Pelz F(x,y) = one of an infinite functions of (x,y)

© 2000 Jeff B. Pelz One-dimensional F(x) = square(x)

© 2000 Jeff B. Pelz F(x) = square(x) sin(x)

© 2000 Jeff B. Pelz F(x) = square(x) sin(x)

© 2000 Jeff B. Pelz F(x) = sin(x) + 1 / 3 sin(3x)

© 2000 Jeff B. Pelz F(x) = sin(x) + 1 / 3 sin(3x) + 1 / 5 sin(5x)

© 2000 Jeff B. Pelz F(x) = sin(x) + 1 / 3 sin(3x) + 1 / 5 sin(5x) + 1 / 7 sin(7x)

© 2000 Jeff B. Pelz F(x) = sin(x) + 1 / 3 sin(3x) + 1 / 5 sin(5x) + 1 / 7 sin(7x) + 1 / 9 sin(9x)

© 2000 Jeff B. Pelz F(x) = sin(x) + 1 / 3 sin(3x) + 1 / 5 sin(5x) + 1 / 7 sin(7x) + 1 / 9 sin(9x) + 1 / 11 sin(11x)

© 2000 Jeff B. Pelz 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)

© 2000 Jeff B. Pelz F(x) = sin(x) + 1 / 3 sin(3x) + 1 / 5 sin(5x) + 1 / 7 sin(7x) + 1 / 9 sin(9x) + …... + 1 / 25 sin(25x)

© 2000 Jeff B. Pelz 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]

© 2000 Jeff B. Pelz F( ) = (1, 1) +( 1 / 3,3) +( 1 / 5, 5) + ( 1 / 7, 7) + ( 1 / 9, 9) + …...

© 2000 Jeff B. Pelz F( ) = 1, 0, 1 / 3, 0, 1 / 5, 0, 1 / 7, 0, 1 / 9, …... Spatial domain Frequency domain

© 2000 Jeff B. Pelz Fourier Pairs

© 2000 Jeff B. Pelz Fourier Pairs

© 2000 Jeff B. Pelz Fourier Pairs

© 2000 Jeff B. Pelz Fourier Pairs

© 2000 Jeff B. Pelz Fourier Pairs

© 2000 Jeff B. Pelz Fourier Pairs

© 2000 Jeff B. Pelz Fourier Pairs

© 2000 Jeff B. Pelz Fourier Pairs

© 2000 Jeff B. Pelz Fourier Pairs

© 2000 Jeff B. Pelz Low-pass Filtering

© 2000 Jeff B. Pelz High-pass Filtering

© 2000 Jeff B. Pelz Frequency Channels