z transform

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z transform

• z transformation transforms linear difference
  equation into algebraic in s.
• Laplace transformation transforms linear
  time-invariant differential equation into
  algebraic in z.

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In time domain
x(t)
y(t)
H(t)
In s domain
x(s)
y(s)

G(s)
-
H(s)
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The z transform method allows

• Conventional analysis and design techniques
• Root-locus
• Frequency response analysis (convert z to w)
• Z transformed characteristic equation allows
  Simple stability test

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Elementary Functions

• Unit-step
• Unit-ramp
• Polynomial
• Exponential
• Sinusoidal
• Table of z transforms (Ogata p-29)

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Important properties

• Multiplication by a constant
• Linearity of z transform
• Multiplication by ak
• Shifting theorem
• Complex translation theorem
• Initial value theorem
• Final value theorem

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Poles and Zeros in the z plane
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Exercise 1

• Ogata
• B-2-1
• B-2-2