Image Fourier Transform

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Image Fourier Transform

• Faisal Farooq

Q How many signal processing engineers does it
take to change a light bulb?
A Three. One to Fourier transform the light
bulb, one to apply a complex exponential
rotational shifting operator, and one to inverse
transform the removed light bulb
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What is frequency domain analysis ?

• Analyzes the signals in the frequency space.
• Primarily involves interpreting the spectrum.

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What are the techniques?

• Fourier Series
• Fourier Transforms
• Discrete Cosine Transform

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Fourier Series

• A Fourier Series is an expansion of a periodic
  function f(x) in terms of an infinite sum of
  sines and cosines.
• Every periodic function can be represented as a
  sum of sine and cosine components. Why?

Trust me!!!
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Examples
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Fourier Transform
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Representation

• Energy Map
• Frequency Map
• Log(Abs(FT)), Why?
• Demo

Dont just trust me!
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Document Images and FT
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Matlab Demos

• 1D Signal Spectrum interpretation
• 1D Signal Filtering
• 2D Signal Spectrum interpretation
• 2D Signal Filtering

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Discrete Cosine Transform

• Similar to Fast Fourier Transform(FFT)
• Note FT N2 , FFT NlgN

• Read Up!

• Next Hough Transform and Moments
• Thank You!