Thursday, March 09, 2006

Several tips about Laplace and Z-transform

  • Negative infinity in s-plane ---- Origin in z-plane
  • Imaginary axis in s-plane ----Unit circle in z-plane
  • Positive infinity in s-plane ---- Positive infinity in z-plane
That also means:
  • left half s-plane ---- Inside the unit circle in z-plane
  • Right half s-plane ---- outside the unit circle in z-plane
  • Imaginary axia in s-plane ---- On unit circle in z-plane
  • H(s) is BIBO stable if all poles are on the left half plane
  • H(z) is BIBO stable if all poles are insde UC
  • Fourier transform in s-plane is evaluated along jw-axis
  • Fourier transform in z-plane is evaluated along UC

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