How the Fourier Transform

Lecture 4: Digital Signal What?

18/10/2004
Summary:
  • Uniform Circular Motion and Simple Harmonic Motion
    • Two SHMs give UCM
    • Two UCMs give SHM
  • Orthogonal bases
    • Simple to invert
  • Fourier series
    • A function as a set of SHMs
    • Complete basis (Dirichlet conditions)
    • Orthogonal basis (Simple to measure)
  • e
    • Compound interest compounded instantaneously
    • Converts geometric series to continuous curve
    • Rate of change is directly proportional to value
    • When rate of change is perpendicular to value, we get unit complex valued UCM
    • This happens when the constant of proportionality is j
    • ejt=cost+jsint
    • ejπ+1=0