Signals and Systems Using MATLAB Luis F. Chaparro

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Signals and SystemsUsing MATLABLuis F.
Chaparro
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Chapter 9 - The Z-transform
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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

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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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