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Homework 2 - Linear System Analysis II | ECE 312, Study notes of Electrical and Electronics Engineering

Colorado State University (CSU)Electrical and Electronics Engineering

Prof. Jie Luo

Homework 2 Material Type: Notes; Professor: Luo; Class: Linear System Analysis II; Subject: Electrical and Computer Engineering; University: Colorado State University; Term: Spring 2015;

Typology: Study notes

2014/2015

Uploaded on 03/28/2015

calebbegly 🇺🇸

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Colorado State University, Ft. Collins

Spring 2015

ECE 312: Linear Systems Analysis II (Signal

and Systems)

Homework 2

Assigned on: 02/17/ 2015, Due by: 03/03/2015

2.1

Consider the system S characterized by the differential equation

         

txty

tdy

tyd

tyd  6116

(a) Determine the zero-state response of this system for the

input

   

tuetx

t4



(b) Determine the zero-input response of the system for

0t

given that

 

10 y

 



t

tdy

 



t

tyd

   

tuetx

t4



and the initial conditions are the same as those specified

in part (b).

2.2

Find the inverse Laplace transform of the function

   





for the following regions of convergence:

(a)

 

1Re s

(b)

 

0Re s

Discover Study notes of Electrical and Electronics Engineering Colorado State University (CSU)

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Download Homework 2 - Linear System Analysis II | ECE 312 and more Study notes Electrical and Electronics Engineering in PDF only on Docsity!

Colorado State University, Ft. Collins

Spring 2015

ECE 312: Linear Systems Analysis II (Signal

and Systems)

Homework 2

Assigned on: 02/17/ 2015, Due by: 03/03/

Consider the system S characterized by the differential equation

y  t  x  t 

dt

dy t

dt

d y t

dt

d y t

2 3 3

(a) Determine the zero-state response of this system for the

input x ^^ t ^  e^ ^4 tu ^ t .

(b) Determine the zero-input response of the system for t  0 ,

given that

y  0   1 ,

1 0   dt t  dy t

1 0 2 2  dt t  d y t

(c) Determine the output of S when the input is x ^^ t ^ e u ^ t 

 ^4 t

and the initial conditions are the same as those specified

in part (b).

Find the inverse Laplace transform of the function

ss s F s

for the following regions of convergence:

(a) Re^ s ^ ^1

(b) Re^ s ^ ^0

(c) ^1 Re^ s ^ ^0

(d) Give the final values of the functions of Parts (a), (b),

and (c).

Consider an LTI system for which we are given the following

information. For input

s s

X s with x  t   0 for t  0 ,

the output of the system is

y  t   et^ u   t   e  tu  t 

(a) Determine H^ ^ s  and its region of convergence

(b) Determine h ^ t 

(c) Using the system function H^ ^ s  found in part (a),

determine the output y^ ^ t  if the input is

x  t   e 3 t for   t .

A pressure gauge that can be modeled as an LTI system has a

time response to a unit step input given by ^ e^ te  u^ ^ t 

1  ^ t^   t

Homework 2 - Linear System Analysis II | ECE 312, Study notes of Electrical and Electronics Engineering

Related documents

Partial preview of the text

Download Homework 2 - Linear System Analysis II | ECE 312 and more Study notes Electrical and Electronics Engineering in PDF only on Docsity!

Colorado State University, Ft. Collins

Spring 2015

ECE 312: Linear Systems Analysis II (Signal

and Systems)

Homework 2

Assigned on: 02/17/ 2015, Due by: 03/03/

Consider the system S characterized by the differential equation

y  t  x  t 

dt

dy t

dt

d y t

dt

d y t

(a) Determine the zero-state response of this system for the

input x ^^ t ^  e^ ^4 tu ^ t .

(b) Determine the zero-input response of the system for t  0 ,

given that

y  0   1 ,

(c) Determine the output of S when the input is x ^^ t ^ e u ^ t 

and the initial conditions are the same as those specified

in part (b).

Find the inverse Laplace transform of the function

for the following regions of convergence:

(a) Re^ s ^ ^1

(b) Re^ s ^ ^0

(c) ^1 Re^ s ^ ^0

(d) Give the final values of the functions of Parts (a), (b),

and (c).

Consider an LTI system for which we are given the following

information. For input

X s with x  t   0 for t  0 ,

the output of the system is

y  t   et^ u   t   e  tu  t 

(a) Determine H^ ^ s  and its region of convergence

(b) Determine h ^ t 

(c) Using the system function H^ ^ s  found in part (a),

determine the output y^ ^ t  if the input is

x  t   e 3 t for   t .

A pressure gauge that can be modeled as an LTI system has a

time response to a unit step input given by ^ e^ te  u^ ^ t 

. For a

certain input x ^^ t , the output is observed to be  2  3 e ^ t^  e ^3 t  u  t .

For this observed measurement, determine the true pressure

input to the gauge as a function of time.

Let H^ ^ s  represent the system function of a causal, stable

system. The input to the system consists of the sum of three

terms, one of which is an impulse ^ ^ t  and another a complex

exponential of the form e s^0 t , where s^ 0 is a complex constant.

The output is