ColorGrayscale Jeffrey Schiano 2014. All rights reserved. Rec 8. EE 350Continuous-Time Linear SystemsRecitation 81 Jeffrey Schiano 2014. All rights reserved. Rec 8. Recitation 8 Topics• Exam II Review2 Jeffrey Schiano 2014. All rights reserved. Rec 8. Problem 1• A certain LTI system has the impulse response1. Is the system causal or noncausal?2. Is the system BIBO stable?3() cos(t 1)u(t 1)tht e Jeffrey Schiano 2014. All rights reserved. Rec 8. Problem 1 Solution4 Jeffrey Schiano 2014. All rights reserved. Rec 8. Problem 1 Solution5 Jeffrey Schiano 2014. All rights reserved. Rec 8. Problem 2• Consider a LTI system with the input f(t) and zero-state response y(t) shown below• Determine the impulse response representation of the system6(1)f( ) 3 ( 1)y( ) 6 u(t 1)ttutte Jeffrey Schiano 2014. All rights reserved. Rec 8. Problem 2 Solution7 Jeffrey Schiano 2014. All rights reserved. Rec 8. Problem 2 Solution8 Jeffrey Schiano 2014. All rights reserved. Rec 8. Problem 3• The system shown below is composed of three LTI systems whose impulse responses are• Determine an impulse response h(t) that represents the composite system so that9312 3( ) ( 2); ( ) sin( ) ( ); h ( ) ( )th t t h t tut t e ut () () ()yt f t ht1()ht2()ht3()ht()ytf( )t Jeffrey Schiano 2014. All rights reserved. Rec 8. Problem 3 Solution10 Jeffrey Schiano 2014. All rights reserved. Rec 8. • Consider a LTI system represented by the ODE• Determine the impulse response representation h(t) of the system 11448()yyyft Problem 4 Jeffrey Schiano 2014. All rights reserved. Rec 8. Problem 4 Solution12 Jeffrey Schiano 2014. All rights reserved. Rec 8. Problem 4 Solution13 Jeffrey Schiano 2014. All rights reserved. Rec 8. Problem 5• A LTI system has the impulse response• The system is driven by the input• Determine the zero-state response y(t) by evaluating the convolution integral using the graphical approach14() 2 ( 2) 4 () 2 ( 2)ht ut ut ut (2)f( ) ( 2)tte ut Jeffrey Schiano 2014. All rights reserved. Rec 8. Problem 5 Solution15 Jeffrey Schiano 2014. All rights reserved. Rec 8. Problem 5 Solution16 Jeffrey Schiano 2014. All rights reserved. Rec 8. Problem 5 Solution17 Jeffrey Schiano 2014. All rights reserved. Rec 8. Problem 5 Solution18 Jeffrey Schiano 2014. All rights reserved. Rec 8. Problem 6• Determine the frequency response function of the network shown below and pace your answer in the standard form191RLftytC2R11101110() () ()()() () ()mmmmnnnbb bbHaaa Jeffrey Schiano 2014. All rights reserved. Rec 8. Problem 6 Solution20 Jeffrey Schiano 2014. All rights reserved. Rec 8. Problem 6 Solution21 Jeffrey Schiano 2014. All rights reserved. Rec 8. Problem 6 Solution22 Jeffrey Schiano 2014. All rights reserved. Rec 8. Problem 7• Determine the sinusoidal state steady response23()yt0() cos( )ftA tLTI()Hj Jeffrey Schiano 2014. All rights reserved. Rec 8. Problem 7 Solution24 Jeffrey Schiano 2014. All rights reserved. Rec 8. Problem 7 Solution25 Jeffrey Schiano 2014. All rights reserved. Rec 8. Problem 8• Consider the two following two signals that are defined over the interval [-1,1] where a and b are nonzero positive real-valued coefficients1. Are the signals orthogonal?2. Determine the value of the parameters a and b for which the signals are orthonormal262132()()tattbt Jeffrey Schiano 2014. All rights reserved. Rec 8. Problem 8 Solution27 Jeffrey Schiano 2014. All rights reserved. Rec 8. Problem 8 Solution28 Jeffrey Schiano 2014. All rights reserved. Rec 8. Problem 9• Write a primary MATLAB function that appreciates the exponential function using the first 100 terms in the taylorseries expansion• The user must be able to call the function using the syntax• Verify your result using MATLAB2910000(x)!!nnxnnxxfenn >> x = -1;>> f_approx = approx_exp(x); Jeffrey Schiano 2014. All rights reserved. Rec 8. EE 350Continuous-Time Linear SystemsRecitation 81 Jeffrey Schiano 2014. All rights reserved. Rec 8. Recitation 8 Topics• Exam II Review2 Jeffrey Schiano 2014. All rights reserved. Rec 8. Problem 1• A certain LTI system has the impulse response1. Is the system causal or noncausal?2. Is the system BIBO stable?3 Jeffrey Schiano 2014. All rights reserved. Rec 8. Problem 1 Solution4 Jeffrey Schiano 2014. All rights reserved. Rec 8. Problem 1 Solution5 Jeffrey Schiano 2014. All rights reserved. Rec 8. Problem 2• Consider a LTI system with the input f(t) and zero-state response y(t) shown below• Determine the impulse response representation of the system6 Jeffrey Schiano 2014. All rights reserved. Rec 8. Problem 2 Solution7 Jeffrey Schiano 2014. All rights reserved. Rec 8. Problem 2 Solution8 Jeffrey Schiano 2014. All rights reserved. Rec 8. Problem 3• The system shown below is composed of three LTI systems whose impulse responses are• Determine an impulse response h(t) that represents the composite system so that9 Jeffrey Schiano 2014. All rights reserved. Rec 8. Problem 3 Solution10 Jeffrey Schiano 2014. All rights reserved. Rec 8. • Consider a LTI system represented by the ODE• Determine the impulse response representation h(t) of the system 11Problem 4 Jeffrey Schiano 2014. All rights reserved. Rec 8. Problem 4 Solution12 Jeffrey Schiano 2014. All rights reserved. Rec 8. Problem 4 Solution13 Jeffrey Schiano 2014. All rights reserved. Rec 8. Problem 5• A LTI system has the impulse response• The system is driven by the input• Determine the zero-state response y(t) by evaluating the convolution
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