Sampling theory, aliasing

CS 248 - Introduction to Computer Graphics
Autumn Quarter, 2004
Marc Levoy
Lecture notes for Thursday, October 7 (second half of class)

Table of contents:

• Sampling and reconstruction
  1. Overview
  2. Looking at venetian blinds through a screen (sampling)
  3. Solution A: finer screen (raising the sampling rate)
  4. Solution B: blur the venetians (bandlimiting)
  5. Example of convolution: rect function
     Facts about convolution
  6. Looking at a photo of the scene mounted on the screen (reconstruction)
  7. Aliasing versus reconstruction error
• Application to computer graphics
  1. Spatial aliasing: polygon edges
  2. Temporal aliasing: wagon wheels
• Frequency domain analysis of sampling (a quick tour)
  • Spectral representations
  • Fourier series: periodic functions
  • Example: sum of sines
  • Spectra: a pair of graphs
  • Representation using complex exponentials
  • Fourier integral: aperiodic functions
  • Fourier transform
  • Example of a transform: box and sinc
  • Dualities