Fourier Demonstration

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Fourier Synthesis
Sinusoidal Functions as Building Blocksfor
Spatial Vision
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Sinusoidal Function F(?) sin(?)
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sin(?)
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sin(0) 0.0
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sin(45) 0.7
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sin(90) 1.0
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sin(135) 0.7
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sin(180) 0.0
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sin(225) - 0.7
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sin(270) - 1.0
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sin(315) - 0.7
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sin(360) sin(0) 0.0
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F(x) sin(x)
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F(x) sin(x)
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F(x) sin(x)
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F(x) sin(x)
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F(x) sin(x)
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F(x) square(x)
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Two-dimensional F(x,y)
Vertical position (y)
Horizontal position (x)
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Two-dimensional F(x,y)
Vertical position (y)
Horizontal position (x)
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F(x,y) one of an infinite functions of (x,y)
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One-dimensional F(x) square(x)
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F(x) square(x) ? sin(x)
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F(x) square(x) ? sin(x)
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F(x) sin(x)1/3 sin(3x)
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F(x) sin(x)1/3 sin(3x) 1/5 sin(5x)
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F(x) sin(x)1/3 sin(3x) 1/5 sin(5x) 1/7
sin(7x)
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F(x) sin(x)1/3 sin(3x) 1/5 sin(5x) 1/7
sin(7x) 1/9 sin(9x)
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F(x) sin(x)1/3 sin(3x) 1/5 sin(5x) 1/7
sin(7x) 1/9 sin(9x) 1/11 sin(11x)
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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)
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F(x) sin(x)1/3 sin(3x) 1/5 sin(5x) 1/7
sin(7x) 1/9 sin(9x) ... 1/25 sin(25x)
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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
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F(?) (1 , 1)(1/3 ,3) (1/5 , 5) (1/7 , 7)
(1/9 , 9) ...
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F(?) 1, 0, 1/3, 0, 1/5 , 0, 1/7 , 0, 1/9, ...
Frequency domain
Spatial domain
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Fourier Pairs
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Fourier Pairs
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Fourier Pairs
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Fourier Pairs
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Fourier Pairs
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Fourier Pairs
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Fourier Pairs
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Fourier Pairs
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Fourier Pairs
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Low-pass Filtering
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High-pass Filtering
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Frequency Channels
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2D Gabor Functions
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