# Signals and Systems Using MATLAB Luis F. Chaparro - PowerPoint PPT Presentation

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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
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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
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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