Convolution

Lecture 1: Digital Signal What?

• Almost everything going into a computer is a signal.
• Scatter filtering
  • Each element uses the same "scatter rule" (filter kernel)
  • It's called convolution
• To be useful, a mathematical theory should be
  1. Easy to apply.
  2. Applicable to a lot of circumstances.
• Examples of convolution
  • Echo
  • Multiple echo
  • Waveguides (Skew, Inter-symbol interference)
  • Any place where you have multi-path conduction
  • Springs
• Gather filtering
  • Equivalent to scatter filtering
  • The gather filter kernel is a left-right flip of the scatter filter kernel
  • The gather view of filtering makes it easy to derive formula for convolution
• Strength theorem