Soln02 - ECE 342 Communication Theory Fall 2005, Solutions...

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Unformatted text preview: ECE 342 Communication Theory Fall 2005, Solutions to Homework 2 Prof. Tiffany J Li www: http://www.eecs.lehigh.edu/ jingli/teach email: jingli@ece.lehigh.edu Problem 2.10 1) Using the Fourier transform pair e- | t | F- 2 2 + (2 f ) 2 = 2 4 2 1 2 4 2 + f 2 and the duality property of the Fourier transform: X ( f ) = F [ x ( t )] x (- f ) = F [ X ( t )] we obtain 2 4 2 F " 1 2 4 2 + t 2 # = e- | f | With = 2 we get the desired result F 1 1 + t 2 = e- 2 | f | 2) F [ x ( t )] = F [( t- 3) + ( t + 3)] = sinc( f ) e- j 2 f 3 + sinc( f ) e j 2 f 3 = 2sinc( f ) cos(2 3 f ) 3) F [ x ( t )] = F [(2 t + 3) + (3 t- 2)] = F [(2( t + 3 2 )) + (3( t- 2 3 )] = 1 2 sinc 2 ( f 2 ) e jf 3 + 1 3 sinc 2 ( f 3 ) e- j 2 f 2 3 4) T ( f ) = F [sinc 3 ( t )] = F [sinc 2 ( t )sinc( t )] = ( f ) ? ( f ). But ( f ) ? ( f ) = Z - ( )( f- ) d = Z 1 2- 1 2 ( f- ) d = Z f + 1 2 f- 1 2 ( v ) dv 1 For f -...
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This note was uploaded on 08/06/2008 for the course ECE 342 taught by Professor Li during the Fall '05 term at Lehigh University .

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Soln02 - ECE 342 Communication Theory Fall 2005, Solutions...

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