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

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

What are the techniques?  Fourier Series  Fourier Transforms  Discrete Cosine Transform

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!!!

Examples

Fourier Transform

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

Document Images and FT

Matlab Demos  1D Signal Spectrum interpretation  1D Signal Filtering  2D Signal Spectrum interpretation  2D Signal Filtering

Discrete Cosine Transform  Similar to Fast Fourier Transform(FFT)  Note: FT = N 2, FFT = NlgN Read Up! Next: Hough Transform and Moments Thank You!