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Signals and Systems Using MATLAB Luis F. Chaparro

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Signals and Systems Using MATLAB Luis F. Chaparro 2 Chapter 9 - The Z-transform 3 What is in this chapter? Laplace transform of sampled signals and Z-transform Two ... – PowerPoint PPT presentation

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Title: Signals and Systems Using MATLAB Luis F. Chaparro


1
Signals and SystemsUsing MATLABLuis F.
Chaparro
2
Chapter 9 - The Z-transform
2
3
What is in this chapter?
  • Laplace transform of sampled signals and
    Z-transform
  • Two- and one-sided Z-transforms
  • Poles and zeros and region of convergence
  • Convolution sum and transfer function
  • Inverse Z-transform
  • Solution of difference and differential equations

3
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Laplace transform of sampled signals
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Two-sided and one-sided Z-transform
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Poles and Zeros
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Convolution Sum and Transfer Function
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Interconnection of discrete-time systems
Cascade
Parallel
Negative feedback
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One-sided Z-transform Inverse
Inspection
Long-division
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Partial Fraction Expansion
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Partial Fraction Expansion with MATLAB
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Example
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Solution of Difference Equations
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Solution of Differential Equations
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Inverse of Two-sided Z-transforms
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What have we accomplished?
  • Connection of Laplace and Z-transforms
  • Significance of poles and zeros in z-plane and
    poles for ROC
  • Solution of difference and differential
    equations with initial conditions
  • Transfer function of recursive and non-recursive
    filters

Where do we go from here?
  • Fourier analysis of discrete-time systems
  • Frequency representation of discrete-time systems
  • Application of Z-transform to control

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