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Image Fourier Transform

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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Image Fourier Transform

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  1. 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

  2. What is frequency domain analysis ? • Analyzes the signals in the frequency space. • Primarily involves interpreting the spectrum.

  3. What are the techniques? • Fourier Series • Fourier Transforms • Discrete Cosine Transform

  4. 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!!!

  5. Examples

  6. Fourier Transform

  7. Representation • Energy Map • Frequency Map • Log(Abs(FT)), Why? • Demo Don’t just trust me!

  8. Document Images and FT

  9. Matlab Demos • 1D Signal Spectrum interpretation • 1D Signal Filtering • 2D Signal Spectrum interpretation • 2D Signal Filtering

  10. Discrete Cosine Transform • Similar to Fast Fourier Transform(FFT) • Note: FT = N2 , FFT = NlgN • Read Up! Next: Hough Transform and Moments Thank You!

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