A#09 - Assignment #9 ECSE-2410 Signals & Systems -...

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Unformatted text preview: Assignment #9 ECSE-2410 Signals & Systems - Fall 2006 In all the problems below, use properties. No integrations of the defining equation. 1(15). Find the Fourier transform of x(t ) = p (t ) cos(t ) , where p (t ) = u (t ) - u (t - 2 ) . Due Fri 10/06/06 1 - - 2 , - 2 < 1 2(15). Sketch the Fourier transform of w(t ) = x(t ) cos(3t ) , where X ( ) = 1 - + 2 , + 2 < 1 0, else 3(40). Find, x(t ) , the inverse Fourier transform for the following signals: (a) 2 1 -2 -1 -1 -2 1 2 3 1 X() (b) X() (c) 1 - e - j 2 1 + j -4 -3 -2 -1 1 2 3 4 X ( ) = (d) X ( ) = 2 ( ) + ( - 4 ) + ( + 4 ) . (e) X ( ) = 6sinc(3( - 2 )) . (f) X ( ) = cos(4 + ) 3 (g) X ( ) = 2[ ( - 1) - ( + 1)] + 3[ ( - 2 ) + ( + 2 )] (h) X ( ) = 1 - e-j 2 j 4(15). Find the inverse Fourier transforms of the following signals: (a) X ( ) = 1 (2 + j )(3 + j ) (b) X ( ) = 1 + e j 2 (2 + j )(3 + j ) (c) X ( ) = j (2 + j )(3 + j ) 5(15). If the impulse response of a LTI system is h(t ) = 2sinc (t ) cos( 4t ) , find output y (t ) , when the input is x(t ) = 1 + cos(t ) + sin( 4t ) ...
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