Lecture 8 Topics

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Lecture 8 Topics

• Fourier Transforms
• As the limit of Fourier Series
• Spectra
• Convergence of Fourier Transforms
• Fourier Transform
• Synthesis equation
• Analysis equation

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We defined
Note that
is the Laplace Transform
is the Fourier Transform
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Relate this to Fourier Series for x(t) periodic,
period
Where
so each term has a gain and phase due to
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Recall from last lecture
x(t)
y(t)
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Recall from last lecture
x(t)
y(t)
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Recall from last lecture
x(t)
y(t)
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Recall from last lecture
x(t)
y(t)
where
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Fourier Transform Limit of Fourier Series
..
..
Fourier Series
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Recall (Euler)
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