A#05 - Given the system impulse response the step response...

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Assignment #5 Due Fri 09/15/06 1(30). Find the equation and sketch the resulting convolution, ) ( ) ( ) ( t b t a t w = , where 2(35). The input-output relationship of an LTI system is governed by the differential equation, ) ( 2 ) ( 2 ) ( t x t y dt t dy = + . Assume the system is causal and is in a condition of initial rest, so that 0 ) 0 ( = y . (a) Solve this differential equation when the input is a unit step function. Recall that in classical solution of differential equations, the step input is treated as a constant of unity for 0 t . (b) Using the results from (a), find the system impulse response, ) ( t h . (c) Find the step response of this system by convolution, ) ( ) ( ) ( t h t x t y = , using the ) ( t h found in (b). (d) Is the following true or false?
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Unformatted text preview: Given the system impulse response, the step response found by solving the differential equation is the same as the one solved by convolution. In other words, convolution is nothing more than the particular solution of the differential equation! 3(35). Solve the differential equation, ), sin( ) ( 2 ) ( = + t t t y dt t dy , with ) ( = y , using classical techniques. Express your answer in the form, ) sin( ) ( + + =-t B Ae t y t . You need to find the numbers for the unknown constants, , , , B A . Express the phase shift, , in degrees. 1 t-1 ) ( t a 1 1 t-1 ) ( t b 1 ) ( t x LTI ) ( t y...
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