EE 350 Continuous-Time Linear Systems Recitation 8

Rec 8.School of Electrical Engineering and Computer Science

Jeffrey Schiano 2015-2017 All rights reserved.

EE 350

Continuous-Time Linear Systems

Recitation 8

1



Recitation 8 Topics

• Exam II Review

2



Problem 1• A certain LTI system has the impulse response

1. Is the system causal or noncausal?

2. Is the system BIBO stable?

3

( ) cos(t 1)u(t 1)th t e



Problem 1 Solution

4



Problem 1 Solution

5



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 system

6

( 1)

( ) 3 ( 1)

( ) 6 ( 1)t

f t u t

y t e u t



Problem 2 Solution

7



Problem 2 Solution

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 that

9

31 2 3( ) ( 2); ( ) sin( ) ( ); h ( ) ( )th t t h t t u t t e u t

( ) ( ) ( )y t f t h t

1( )h t2 ( )h t

3 ( )h t

( )y tf( )t



Problem 3 Solution

10



• Consider a LTI system represented by the ODE

• Determine the impulse response representation h(t) of the system

11

4 4 8 ( )y y y f t

Problem 4



Problem 4 Solution

12



Problem 4 Solution

13



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 approach

14

( ) 2 ( 2) 4 ( ) 2 ( 2)h t u t u t u t

( 2)f( ) ( 2)tt e u t



Problem 5 Solution

15



Problem 5 Solution

16



Problem 5 Solution

17



Problem 5 Solution

18



Problem 6• Determine the frequency response function of the

network shown below and pace your answer in the standard form

19

1RL

f t y t

C

2R

11 1 0

11 1 0

( ) ( ) ( )( )( ) ( ) ( )

m mm m

n nn

b b b bHa a a



Problem 6 Solution

20



Problem 6 Solution

21



Problem 6 Solution

22



Problem 7• Determine the sinusoidal state steady response

23

( )y t0( ) cos( )f t A t LTI( )H j



Problem 7 Solution

24



Problem 7 Solution

25



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 coefficients

1. Are the signals orthogonal?

2. Determine the value of the parameters a and bfor which the signals are orthonormal

26

21

32

( )

( )

t at

t bt



Problem 8 Solution

27



Problem 8 Solution

28



Problem 9• Write a primary MATLAB function that approximates

the exponential function using the first 100 terms in the Taylor series expansion

• The user must be able to call the function using the syntax

• Verify your result using MATLAB29

100

0 0

(x)! !

n nx

n n

x xf en n

>> x = -1;>> f_approx = approx_exp(x);



EE 350

Continuous-Time Linear Systems

Recitation 8

1



Recitation 8 Topics

• Exam II Review

2



Problem 1• A certain LTI system has the impulse response

1. Is the system causal or noncausal?

2. Is the system BIBO stable?

3



Problem 1 Solution

4



Problem 1 Solution

5



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 system

6



Problem 2 Solution

7



Problem 2 Solution

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 that

9



Problem 3 Solution

10



• Consider a LTI system represented by the ODE

• Determine the impulse response representation h(t) of the system

11

Problem 4



Problem 4 Solution

12



Problem 4 Solution

13



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 approach

14



Problem 5 Solution

15



Problem 5 Solution

16



Problem 5 Solution

17



Problem 5 Solution

18



Problem 6• Determine the frequency response function of the

network shown below and pace your answer in the standard form

19



Problem 6 Solution

20



Problem 6 Solution

21



Problem 6 Solution

22



Problem 7• Determine the sinusoidal state steady response

23



Problem 7 Solution

24



Problem 7 Solution

25



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 coefficients

1. Are the signals orthogonal?

2. Determine the value of the parameters a and bfor which the signals are orthonormal

26



Problem 8 Solution

27



Problem 8 Solution

28



Problem 9• Write a primary MATLAB function that approximates

the exponential function using the first 100 terms in the Taylor series expansion

• The user must be able to call the function using the syntax

• Verify your result using MATLAB29

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EE 350 Continuous-Time Linear Systems Recitation 8