Some Example Con tin uous ourier transforms    dt Giv en that  dt   dt   dt Therefore   Linearit of the ourier transform   where is constan Using the dualit prop ert and the linearit prop ert of the
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Some Example Con tin uous ourier transforms dt Giv en that dt dt dt Therefore Linearit of the ourier transform where is constan Using the dualit prop ert and the linearit prop ert of the

brPage 9br 6 ft 6 2 4 0 0 0 0 0 0 w 0 0 2p Figure 4 sinct and its ourier transform An imp ortan oin is that signal that is bandlimited is not timelimited while signal that is timelimited is not bandlimited

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Some Example Con tin uous ourier transforms dt Giv en that dt dt dt Therefore Linearit of the ourier transform where is constan Using the dualit prop ert and the linearit prop ert of the




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Presentation on theme: "Some Example Con tin uous ourier transforms dt Giv en that dt dt dt Therefore Linearit of the ourier transform where is constan Using the dualit prop ert and the linearit prop ert of the"— Presentation transcript:


Page 1
Some Example Con tin uous ourier transforms )) )) 1 dt Giv en that 1 dt (0) 1 dt (0) 1 dt Therefore ))
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Linearit of the ourier transform )) ), where is constan Using the dualit prop ert and the linearit prop ert of the ourier transform A ourier transform of at (see Figure 1)
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at dt 1/a p/2 p/2 Magnitude Phase −at Figure 1: The exp onen tial function and its ourier transform
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ourier transform of the unit step function The ourier transform of the unit step function can obtained only in the

limit )) lim at ourier transform of (see Figure 2)
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|a|t 2/a Magnitude F( ) Figure 2: j and its ourier transform
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at at dt 1 dt ourier transform of the rectangular function A; other ise
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Ae dt AT sin sinc The rectangular function ect and its ourier transform are sho wn in Figure
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T AT 2 4 F( ) Figure 3: rect(t) and its ourier transform ourier transform of the sinc function Using the dualit prop ert the ourier transform of the sinc function can determined (see Figure 4).
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6 ......... ......... f(t) 6

2 4 0 0 0 0 0 0 -w 0 0 2p Figure 4: sinc(t) and its ourier transform An imp ortan oin is that signal that is \bandlimited" is not \time-limited" while signal that is \time-limited" is not \bandlimited"