The Discrete Fourier Transform

The fourth week begins with the definition of the discrete Fourier transform, followed by the fast Fourier transform (FFT), and then applications of the FFT in the third lecture of the week.

• Filter Design
  • Roots of Unity
  • Definition of the DFT
  • Convolutions and the DFT
  • Interpolation by the DFT
  • Exercises
  • Bibliography
• The Fast Fourier Transform
  • Time and Frequency Domains
  • The Fast Fourier Transform
  • Filter Design
  • Exercises
  • Bibliography
• Applications of the FFT
  • Spectral Analysis
  • Image Processing
  • Exercises
  • Bibliography
  • Summary of the Last Six Lectures