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# A#11 - -1 X 1 3-2-1 ω 1-2 2 2 10(8 We know that the...

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Assignment #11 ECSE-2410 Signals & Systems - Spring 2009 Due Fri 02/27/09 Use the properties and transform Tables (no integrations of the definition) to solve the following: 1(10). Use duality to find the Fourier transform of ( ) 2 1 1 t t x + = . 2(10). Find the Fourier transform of ( ) 2 3 = t e t x 3(8). Find the Fourier transform of ( ) ( ) ( ) t t t x 2 sinc sinc = 4(10). Find the Fourier transform of ( ) ( ) ( ) = t t dt d t x 2 sinc 2 sinc 1 π π 5(8). Find the inverse transform of ( ) ω ω ω j e X j + = 1 1 . 6(8). Find the inverse transform of ( ) ( ) 1 1 + = ω ω ω j e X j . 7(10). Find the inverse transform of ( ) ( ) ω ω ω j X + = 1 2 cos 2 . 8(8). Find the inverse transform of ( ) ( ) ( ) π ω ω 2 3 sinc 6 = X . 9(10).Find the inverse transform of

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Unformatted text preview: . -1 X ( ) 1 3-2-1 ω 1 -2 2 2 10(8). We know that the inverse transform of is ( ) ( ) t t x 2 sinc 2 1 = . ( ) 1 X 1 1-2-1 0 2 However, if we think of this pulse as made up of two adjacent pulses of width 2, i.e. , as then the inverse Fourier transform is ( ) ( ) ( ) t t t x cos sinc 2 2 = . ( ) 2 X Show that . ( ) ( ) t x t x 2 1 = 11(10). If the impulse response of a LTI system is ) 4 cos( ) ( sinc 2 ) ( t t t h = , find output , when the ) ( t y input is ) 4 sin( ) cos( 1 ) ( t t t x + + = 1 -2 -1 0 1 2...
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