Ch3.2 Discrete Fourier Transform
Ch3.2 Discrete Fourier Transform
Ch3.2 Discrete Fourier Transform
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<strong>Discrete</strong> <strong>Fourier</strong> <strong>Transform</strong><br />
• Example: Determine DFT of the length-N sequence<br />
cos <br />
,01<br />
<br />
• Using the trigonometric identity, we can obtain<br />
/ / = <br />
<br />
• The N-point DFT is given by<br />
∑<br />
<br />
∑ <br />
<br />
<br />
∑<br />
<br />
<br />
• Using the identity, ∑<br />
<br />
<br />
we get <br />
<br />
<br />
<br />
<br />
,for <br />
,for <br />
0, otherwise<br />
, for , an integer<br />
<br />
0, otherwise<br />
Elec3100 Chapter 3<br />
9
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