Fourier Transform

• Fourier Transform is a coordinate transform
• Idea: Approximating a function by a sum of sinusoids of increasing frequencies which form an orthogonal basis for the functions' space

FFT

• It is how you compute a Fourier Series on a computer
• The FFT is a computationally efficient way of computing the DFT
• FFT is synonym to DFT
• Applications:
  • Solve PDEs
  • Denoising Data
  • Data Analysis
  • Compression