# A#05 - (b(5 What is the circuit time constant 4(20...

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Assignment #05 ECSE-2410 Signals & Systems - Spring 2009 Due Fri 01/30/09 1(30). Solve the following first-order differential equations by classical methods. (a)(15) 0 ), sin( ) ( 2 ) ( = + t t t y dt t dy , with 0 ) 0 ( = y . Using the sum- and difference-of-two-angles formulas from trigonometry, express your answer in the form, . Thus, you need to find the values of the unknown constants, ) sin( ) ( θ α + + = t B Ae t y t , , , B A . Express the phase shift, , in degrees. (b)(15) 0 , ) ( ) ( = + t e t y dt t dy t with, 0 ) 0 ( = y . 2(15). A LTI system is described by the differential equation, 0 ), ( ) ( 2 ) ( = + t t x t y dt t dy . LTI () t x ( ) t y Find the system impulse response, ( ) t h . 2 = L 1 = R ( ) t x ( ) t y + + 3(15). (a)(10) Find the input-output differential equation for the circuit.
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Unformatted text preview: (b)(5) What is the circuit time constant? 4(20). Evaluate (a) ( ) ∑ −∞ = − n k k k ] 1 [ 2 1 δ (b) ( ) ∑ ∞ −∞ = − k k k ] 1 [ 2 1 (c) ( ) ∑ ∞ −∞ = − k k k u ] 1 [ 2 1 (d) ( ) ∑ ∞ = − 4 1 ] [ k k k n 5(20). The impulse response of a discrete-time, linear, time-invariant system is shown below. ] [ ] [ n n x = h [ n ] 2 1 LTI 1 1 n n ... ... ... ...-1 0 1 -1 0 1 2 3 Sketch the response of this system when the input is x [ n ]={. ..0,2,1 ,0,. ..}....
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## This note was uploaded on 05/03/2009 for the course ECSE 2410 taught by Professor Wozny during the Spring '07 term at Rensselaer Polytechnic Institute.

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