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Unformatted text preview: Assignment #10 p.1 ECSE-2410 Signals & Systems - Fall 2006 Due Fri 10/13/06 1(10). Suppose we know the Fourier transform pair 2 2 2 1 2 2 ) ( ) ( = = = e X e t x F t , called the Gaussian pulse. Use the duality property developed in class to find the transform of 2 2 ) ( t e t X = . 2(10). Suppose . Find the steady-state response, , to the input ) ( 2 ) ( 2 t u e t h t = ) ( t y ) 2 cos( 2 ) ( t t x + = . Use the steady-state equation derived in class. ( ) H t h 3(25). The input to the system, is the periodic signal shown ) ( t ) ( ) ( t y LTI x 1 2 3 4 0 -1 x ( t ) t 1 (a). Find the equation for ) ( X and plot . ) ( vs X for 5 < . (b). Let ( ) < = , 3 , 1 else H , and sketch . ) ( vs H . (c). Sketch ( ) ( ) ( ) . vs H X Y = for 5 < . (d). Use the plot in (c) to write the equation for . Express exponentials in terms of trigonometric functions (i.e., cosines and/or sines.) functions (i....
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