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Signals and Systems Using MATLAB Luis F. Chaparro

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Page 1: Signals and Systems Using MATLABes413/Slides_20161/SS...Significance of complex exponentials as inputs of LTI systems ... because the zero of the Laplace transform is s tan(O) 2 tan(T/4)

Signals and Systems

Using MATLAB

Luis F. Chaparro

Page 2: Signals and Systems Using MATLABes413/Slides_20161/SS...Significance of complex exponentials as inputs of LTI systems ... because the zero of the Laplace transform is s tan(O) 2 tan(T/4)

Chapter 3 - The Laplace Transform

Page 3: Signals and Systems Using MATLABes413/Slides_20161/SS...Significance of complex exponentials as inputs of LTI systems ... because the zero of the Laplace transform is s tan(O) 2 tan(T/4)

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What is in this chapter?

Definition of Laplace transform

Analysis of LTI systems using Laplace transform

Properties of Laplace transform

Inverse Laplace transform

Convolution integral

Convolution sum and Laplace

System interconnection

Page 4: Signals and Systems Using MATLABes413/Slides_20161/SS...Significance of complex exponentials as inputs of LTI systems ... because the zero of the Laplace transform is s tan(O) 2 tan(T/4)

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Signals and LTI systems

Page 5: Signals and Systems Using MATLABes413/Slides_20161/SS...Significance of complex exponentials as inputs of LTI systems ... because the zero of the Laplace transform is s tan(O) 2 tan(T/4)

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Page 6: Signals and Systems Using MATLABes413/Slides_20161/SS...Significance of complex exponentials as inputs of LTI systems ... because the zero of the Laplace transform is s tan(O) 2 tan(T/4)

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Page 7: Signals and Systems Using MATLABes413/Slides_20161/SS...Significance of complex exponentials as inputs of LTI systems ... because the zero of the Laplace transform is s tan(O) 2 tan(T/4)

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Page 8: Signals and Systems Using MATLABes413/Slides_20161/SS...Significance of complex exponentials as inputs of LTI systems ... because the zero of the Laplace transform is s tan(O) 2 tan(T/4)

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Page 9: Signals and Systems Using MATLABes413/Slides_20161/SS...Significance of complex exponentials as inputs of LTI systems ... because the zero of the Laplace transform is s tan(O) 2 tan(T/4)

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Three

Page 10: Signals and Systems Using MATLABes413/Slides_20161/SS...Significance of complex exponentials as inputs of LTI systems ... because the zero of the Laplace transform is s tan(O) 2 tan(T/4)

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Page 11: Signals and Systems Using MATLABes413/Slides_20161/SS...Significance of complex exponentials as inputs of LTI systems ... because the zero of the Laplace transform is s tan(O) 2 tan(T/4)

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Page 12: Signals and Systems Using MATLABes413/Slides_20161/SS...Significance of complex exponentials as inputs of LTI systems ... because the zero of the Laplace transform is s tan(O) 2 tan(T/4)

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One-sided Laplace Transform

Page 13: Signals and Systems Using MATLABes413/Slides_20161/SS...Significance of complex exponentials as inputs of LTI systems ... because the zero of the Laplace transform is s tan(O) 2 tan(T/4)

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Page 14: Signals and Systems Using MATLABes413/Slides_20161/SS...Significance of complex exponentials as inputs of LTI systems ... because the zero of the Laplace transform is s tan(O) 2 tan(T/4)

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Page 15: Signals and Systems Using MATLABes413/Slides_20161/SS...Significance of complex exponentials as inputs of LTI systems ... because the zero of the Laplace transform is s tan(O) 2 tan(T/4)

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Page 16: Signals and Systems Using MATLABes413/Slides_20161/SS...Significance of complex exponentials as inputs of LTI systems ... because the zero of the Laplace transform is s tan(O) 2 tan(T/4)

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Page 17: Signals and Systems Using MATLABes413/Slides_20161/SS...Significance of complex exponentials as inputs of LTI systems ... because the zero of the Laplace transform is s tan(O) 2 tan(T/4)

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Page 18: Signals and Systems Using MATLABes413/Slides_20161/SS...Significance of complex exponentials as inputs of LTI systems ... because the zero of the Laplace transform is s tan(O) 2 tan(T/4)

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Page 19: Signals and Systems Using MATLABes413/Slides_20161/SS...Significance of complex exponentials as inputs of LTI systems ... because the zero of the Laplace transform is s tan(O) 2 tan(T/4)

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Linearity

Page 20: Signals and Systems Using MATLABes413/Slides_20161/SS...Significance of complex exponentials as inputs of LTI systems ... because the zero of the Laplace transform is s tan(O) 2 tan(T/4)

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Page 21: Signals and Systems Using MATLABes413/Slides_20161/SS...Significance of complex exponentials as inputs of LTI systems ... because the zero of the Laplace transform is s tan(O) 2 tan(T/4)

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Page 22: Signals and Systems Using MATLABes413/Slides_20161/SS...Significance of complex exponentials as inputs of LTI systems ... because the zero of the Laplace transform is s tan(O) 2 tan(T/4)

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Derivative

Page 23: Signals and Systems Using MATLABes413/Slides_20161/SS...Significance of complex exponentials as inputs of LTI systems ... because the zero of the Laplace transform is s tan(O) 2 tan(T/4)

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Page 24: Signals and Systems Using MATLABes413/Slides_20161/SS...Significance of complex exponentials as inputs of LTI systems ... because the zero of the Laplace transform is s tan(O) 2 tan(T/4)

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Page 25: Signals and Systems Using MATLABes413/Slides_20161/SS...Significance of complex exponentials as inputs of LTI systems ... because the zero of the Laplace transform is s tan(O) 2 tan(T/4)

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Time Shifting

Page 26: Signals and Systems Using MATLABes413/Slides_20161/SS...Significance of complex exponentials as inputs of LTI systems ... because the zero of the Laplace transform is s tan(O) 2 tan(T/4)

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Page 27: Signals and Systems Using MATLABes413/Slides_20161/SS...Significance of complex exponentials as inputs of LTI systems ... because the zero of the Laplace transform is s tan(O) 2 tan(T/4)

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Convolution integral

Page 28: Signals and Systems Using MATLABes413/Slides_20161/SS...Significance of complex exponentials as inputs of LTI systems ... because the zero of the Laplace transform is s tan(O) 2 tan(T/4)

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Inverse Laplace Transform

Page 29: Signals and Systems Using MATLABes413/Slides_20161/SS...Significance of complex exponentials as inputs of LTI systems ... because the zero of the Laplace transform is s tan(O) 2 tan(T/4)

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Page 30: Signals and Systems Using MATLABes413/Slides_20161/SS...Significance of complex exponentials as inputs of LTI systems ... because the zero of the Laplace transform is s tan(O) 2 tan(T/4)

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Page 31: Signals and Systems Using MATLABes413/Slides_20161/SS...Significance of complex exponentials as inputs of LTI systems ... because the zero of the Laplace transform is s tan(O) 2 tan(T/4)

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Page 32: Signals and Systems Using MATLABes413/Slides_20161/SS...Significance of complex exponentials as inputs of LTI systems ... because the zero of the Laplace transform is s tan(O) 2 tan(T/4)

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Page 33: Signals and Systems Using MATLABes413/Slides_20161/SS...Significance of complex exponentials as inputs of LTI systems ... because the zero of the Laplace transform is s tan(O) 2 tan(T/4)

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Page 34: Signals and Systems Using MATLABes413/Slides_20161/SS...Significance of complex exponentials as inputs of LTI systems ... because the zero of the Laplace transform is s tan(O) 2 tan(T/4)

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Page 35: Signals and Systems Using MATLABes413/Slides_20161/SS...Significance of complex exponentials as inputs of LTI systems ... because the zero of the Laplace transform is s tan(O) 2 tan(T/4)

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Page 36: Signals and Systems Using MATLABes413/Slides_20161/SS...Significance of complex exponentials as inputs of LTI systems ... because the zero of the Laplace transform is s tan(O) 2 tan(T/4)

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Page 37: Signals and Systems Using MATLABes413/Slides_20161/SS...Significance of complex exponentials as inputs of LTI systems ... because the zero of the Laplace transform is s tan(O) 2 tan(T/4)

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Page 38: Signals and Systems Using MATLABes413/Slides_20161/SS...Significance of complex exponentials as inputs of LTI systems ... because the zero of the Laplace transform is s tan(O) 2 tan(T/4)

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Page 39: Signals and Systems Using MATLABes413/Slides_20161/SS...Significance of complex exponentials as inputs of LTI systems ... because the zero of the Laplace transform is s tan(O) 2 tan(T/4)

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Page 40: Signals and Systems Using MATLABes413/Slides_20161/SS...Significance of complex exponentials as inputs of LTI systems ... because the zero of the Laplace transform is s tan(O) 2 tan(T/4)

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Page 41: Signals and Systems Using MATLABes413/Slides_20161/SS...Significance of complex exponentials as inputs of LTI systems ... because the zero of the Laplace transform is s tan(O) 2 tan(T/4)

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Page 42: Signals and Systems Using MATLABes413/Slides_20161/SS...Significance of complex exponentials as inputs of LTI systems ... because the zero of the Laplace transform is s tan(O) 2 tan(T/4)

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Page 43: Signals and Systems Using MATLABes413/Slides_20161/SS...Significance of complex exponentials as inputs of LTI systems ... because the zero of the Laplace transform is s tan(O) 2 tan(T/4)

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Page 44: Signals and Systems Using MATLABes413/Slides_20161/SS...Significance of complex exponentials as inputs of LTI systems ... because the zero of the Laplace transform is s tan(O) 2 tan(T/4)

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Page 45: Signals and Systems Using MATLABes413/Slides_20161/SS...Significance of complex exponentials as inputs of LTI systems ... because the zero of the Laplace transform is s tan(O) 2 tan(T/4)

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Page 46: Signals and Systems Using MATLABes413/Slides_20161/SS...Significance of complex exponentials as inputs of LTI systems ... because the zero of the Laplace transform is s tan(O) 2 tan(T/4)

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Page 47: Signals and Systems Using MATLABes413/Slides_20161/SS...Significance of complex exponentials as inputs of LTI systems ... because the zero of the Laplace transform is s tan(O) 2 tan(T/4)

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What have we accomplished?

Connection of Laplace and Fourier transforms

BIBO stability and pole location

Steady-state analysis using Fourier for periodic and aperiodic signals

Significance of complex exponentials as inputs of LTI systems

Where do we go from here?

Complex frequency analysis of signals

Convolution integral computation and transfer function

Significance of location of poles and zeros

Sinusoidal representation of periodic signals

Solution of differential equations, transient and steady state responses, zero-

input and zero-state responses