Solve Exercise 1.22 using the concept of the transfer function. Exercise 1.22 Compute the inverse Fourier transform
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Solve Exercise 1.22 using the concept of the transfer function.
Exercise 1.22
Compute the inverse Fourier transform of
\[X\left(\mathrm{e}^{\mathrm{j} \omega}\right)=\frac{1}{1-\mathrm{e}^{-\mathrm{j} \omega}}\]
in Example 2.19.
Hint: Replace \(\mathrm{e}^{\mathrm{j} \omega}\) by \(z\), compute the inverse \(z\) transform using as closed contour \(C\) the one defined by \(z=ho \mathrm{e}^{\mathrm{j} \omega}, ho>1\), and take the limit as \(ho \rightarrow 1\).
Example 2.19.
Compute the Fourier transform of the sequence x(n) = u(n)
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Related Book For
Digital Signal Processing System Analysis And Design
ISBN: 9780521887755
2nd Edition
Authors: Paulo S. R. Diniz, Eduardo A. B. Da Silva , Sergio L. Netto
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