Lab Sept 27

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Lab Sept 27
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review

• Fourier splits a signal into components
• Each component
• Basis function
• Coefficient
• Basis function sine wave at particular freq
• Coefficient amplitude and phase

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review
image taken from wikipedia
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review
perfect sin waves at diff frequencies and
amplitudes
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review
perfect sin waves at diff frequencies and
amplitudes
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review
perfect sin waves at diff frequencies and
amplitudes
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review
perfect sin waves at diff frequencies and
amplitudes
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review
perfect sin waves at diff frequencies and
amplitudes
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review

• Frequency domain graph

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review

• Frequency domain graph

? Number of cycles per area
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review

• Frequency domain graph

? 1 cycle. Height gives amplitude
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review

• Frequency domain graph

? 1 cycle. Height gives amplitude
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review

• Frequency domain graph

? 2 cycle. Height gives amplitude
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review

• Frequency domain graph

? 3 cycles. Height gives amplitude
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review

• Frequency domain graph

? 4 cycle. Height gives amplitude
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review

• Frequency domain graph

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review
spatial
frequency
http//local.wasp.uwa.edu.au/pbourke/other/dft/
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review
spatial
frequency
http//local.wasp.uwa.edu.au/pbourke/other/dft/
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Spatial/frequency domain
spatial
frequency
http//local.wasp.uwa.edu.au/pbourke/other/dft/
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Spatial/frequency domain
spatial
frequency
http//local.wasp.uwa.edu.au/pbourke/other/dft/
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Spatial/frequency domain
spatial
frequency
http//local.wasp.uwa.edu.au/pbourke/other/dft/
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Spatial/frequency domain
spatial
frequency
http//local.wasp.uwa.edu.au/pbourke/other/dft/
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More 2D!

• Spatial domain
• What we are used to

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More 2D!

• Spatial domain

y
x
Pixel colour
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More 2D!

• Frequency domain

v
u
Amplitude/phase
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More 2D!

• Frequency domain

v
u
Amplitude/phase
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More 2D!

• Frequency domain
• u- freq in x direction
• v- freq in y direction
• amplitude is brightness

v
u
Amplitude/phase
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2d images..
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2d images..
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2d images

• Mixed components?

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2d images

• Mixed components?

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Handout quiz!

• Groups!
• Match each spatial graph to its frequency graph
• What is the u, v value of each? Hint, only look
  at spatial graphs for this.

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Pictures?

• Frequency plot too complex to understand
• But! We can see trends and particular properties

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http//www.cs.unm.edu/brayer/vision/fourier.html
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Edge effects

• FFT is periodic
• Assumes image repeats!

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Edge effects

• FFT is periodic
• Assumes image repeats!

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Edge effects

• Why only in y direction?
• Spike perpendicular to strong changes and
  features.

http//www.cs.unm.edu/brayer/vision/fourier.html
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Strong features
http//www.cs.unm.edu/brayer/vision/fourier.html
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Strong features
http//www.cs.unm.edu/brayer/vision/fourier.html
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Handout / quiz 2

• Match the image to the frequency graph