Ch3.2 Discrete Fourier Transform
Ch3.2 Discrete Fourier Transform
Ch3.2 Discrete Fourier Transform
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Inverse <strong>Discrete</strong> <strong>Fourier</strong> <strong>Transform</strong> (IDFT)<br />
• From the definition of the inverse discrete <strong>Fourier</strong> transform<br />
(IDFT), ∑ <br />
.<br />
<br />
• By substituting ∑<br />
<br />
, we can obtain<br />
∑ <br />
∑<br />
<br />
<br />
• Given ∑<br />
<br />
<br />
we have .<br />
<br />
<br />
<br />
<br />
∑ ∑ <br />
<br />
<br />
∑ ∑ <br />
<br />
<br />
, for , an integer<br />
<br />
0, otherwise ,<br />
• Thus, we can reconstruct from .<br />
Elec3100 Chapter 3<br />
7
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