ADAMSON UNIVERSITY

COLLEGE OF ENGINEERING

ELECTRONICS ENGINEERING DEPARTMENT

1ST SEMESTER / S. Y. 2015-2016

EXPERIMENT TITLE : LTI System and Its Response

EXERCISE NUMBER : 5

COURSE CODE : ECE328L

SECTION/SCHEDULE : 59034 / WEDNESDAY 2:00-5:00

GROUP NUMBER : 6

GROUP MEMBERS : HERRERA, Aileen May S.

JUAT, Kathleen Joy DC

_______________________________________

Engr. Rosallie G. De Ocampo

September 9, 2015

1. You want to design a causal LTI system with the property that if the input () = 0.5() 0.25(0.5)1( 1)

Then the output is () = (1

3)()

Find the difference equation that characterize this system

SOLUTION:

() =1

1 0.51

0.251

1 0.51=1 0.251

1 0.51

() =1

1 13

1

() = () [1

()] =

1

1 13

1[1 0.51

1 0.251] =

1 12

1

1 14

1 13

1 +112

2

() =1

12

1

1 712

1 +112

2=

1 12

1

(1 13

1) (1 14

1)

() =

(1 13

1)+

(1 14

1)

Partial Fraction:

1 1

21 = (1

1

41) + (1

1

31) =

1

41 +

1

31

Constant: 1 = +

z-1: 1

2=

1

4 +

1

3

A = -2 ; B = 3

=

+

=

+

() =()

()=

2

(1 13)

+3

(1 14)

=2

3 13

+3

4 14

=6

3 1+

12

4 1

()

()=

122 6

122 7 + 1; ()[122 7 + 1] = ()[122 6]

122() 7() + () = 122() 6()

122

2 7

+ = 12

2

2 6

+ =

2. For each digital filter, use block diagram algebra to solve the following: a. Create the difference equation b. State the order of the filter c. Find H(z)

+

= ()

() +1

42() = ()

[1 +1

42] () = ()

=()

()= +

a. Difference equation: () +

( ) = ()

b. Second order

c. () =()

()= 1 +

1

42

() = () + ( 1) + () (

1)

= ()

() = 2()

= () = 2()

a. Difference equation: () =

2() b. First order

c. () = 2