!

"#

!

$%&'()($$()*+

,-

!"#$%& !"

! ,-

. ((

Chapter-01.p65 11/24/08, 1:50 PM1

!,

/)01-

.

.(1

2!

.(1

. (1

! 3

!4

#

/)(1/)5(51

#

(3,- ,-

' %!"#( %!"

!,-

,-/ ,6- ,((-

,-

,-(

7800

#

9:,((- !

!!,-

,-/ ,5- ,(1-

3129 29

2827

0 1 2 3 4 nT

Chapter-01.p65 11/24/08, 1:50 PM2

3

#3

!,-(0

:1,(0-:,- 9:,((- 9:,(1- 9:((

39:,(1-

!" !

#$#

,-/ ()1,()-/2;(61) !

>:,-.

,-/13=KK

>

"0 ($0 !$

$

,-/( / )

)

0 ...1$

!"

'()*%&'( #

1

(

, - , -

/,-N/)/,)- ,((2-

,-/)(1(1

/)

&

+

% ,-/(

? ( /=1/6

=

( , -

/(,-/(

Chapter-01.p65 11/24/08, 1:50 PM12

"

+, $'&

+

%

)

) =

( , - (

?)#

+,',( +4& & 9

1

(

, - , = - , - , -

"% "&>

1 1

( (

, - , = - , - , = - , -

1 1

( (

, - , = - , - , = -

,-/(1/

,- ,=-/,- ,=-

.

,-

#)

)

,-,-

.((2

$

,-10 =01601#

#,- /)

(#>

.((B

(

. , = )-

),-

'(-%'( ,- O

( ), -

) )

,((B-

x(t)

1/

/2/2 t0

0

"#

1

t0

Chapter-01.p65 11/24/08, 1:50 PM13

"

.((&

,-,-@

,-/

=

, -

,((&-

4

!

=K)#)(

,-/( )

) )

>,-

,-/

=

, -

,((%-

,- /,- ,(($-

$+& & :,

$%

,- , - &

./=*/=(,-

)1( ,-

(/=*/=(

./=(/6(,- ,-#

./(/*,-

=( ,-.((%, -

" ,- ,-

,- /,6*-=,6(-=,=(-6,=*-

J 9:,(($-

, - / ,6*-0 ,((-0 ,0(-( ,0*-

/=*/*

=(/=(/(.((%,-

)* :

,- /6 ,(1)-

6/)J

1

u(t)

t0

x(t)

x(t)

t

t

t

1 0

0

(a)

1

2

1

33

1

1 1

0

(b)

(c)

1

1 1

3

3

1 1 33

x(t)

! 1"#

Chapter-01.p65 11/24/08, 1:51 PM14

"

.(($,-, -

//,- !

t0 0

A

A

t

b = 3

b = 3

b = 2

b = 2b

= 1

b = 1

x(t) x(t)

,- , -

" "#"#

$ .(($,-(($, - :

'.()* 6

6.(1)

,-/3 =

1 1

) 3

6

,(1(-

::

O6,0-6,0-

'.(

,?-,-

,-/6,6- ,(11-6/1 :

'/(

'( )* 0

D ,-E

,- /( )

)

,(1*-

J.(1(

'()*0 !: ! !! D,-E

t

A

x(t)

0T/2 T/2

#

n0 1 2 3

1

123

2

Chapter-01.p65 11/24/08, 1:51 PM15

"

,- /( )

) )

,(1'-

.(11

0 1 2 3 k

1

n12

2

'()*0 !: D,-E

,- /3 )

) 3 )

,(12-

0 1

2

3

4

1

2 3 4

k

k n12

r(n)

2

'.()*0 !

,- /,- ,(1B-

0 1

2

4

8

1

2 3 n12

2$3

(

(:

Chapter-01.p65 11/24/08, 1:51 PM16

"

1

0.64

0.512

1 0 1 2 3 2

0.8

n

2$&4

'.(0 !,-/1

!,-/1 ,- /(0 :/%:

,- /11

/11

%

,(1&-

.(1B

2

2

0 1 2

3 4 5

6 7 8 9 10 n

2, 1$ ,,.

$$3,4

,-,-

!"

'(-/ ?,-,- ',-

',- /,-6,- ,(1%-

'(1%/,

',- /,- ,(1$-

N;P(,-,-

N;K(

Chapter-01.p65 11/24/08, 1:51 PM17

"

'(1%2

',- /,-,- ,(*)-

A:

'.(%% .%,-),-

%,- /, -

)

,(*(-

,-*

%,- /

=

(, -

*

,(*1-

'.(*% @,-,=)-,- ).(1&

x(t) x(t t0)

A A

T t T + t0t00 t0

"#"# "#"#

,-,-#

),-6

#,-#,=)-,=)-K)

K)/)#,=)-6

,=)- ) )6)

=)PP6),=)-#

.,6 )- ,- )

'.(3 L ,- ,- ,-?,-

.(1%,-

x(t) x(2t)

A A

T t T/20 t0

! "#0 ! "#

Chapter-01.p65 11/24/08, 1:51 PM18

"!

!,-,1-

,-

1.(1%, -,)2-

!,-

(0)2/1

45'( Q

! !

.,1=*-

,-.(1%,-/1

,1=*-/,-

#,1=*-K)K*01

(),1=*-1*01201>,1=*-P1

P201 #,-/,1=*-

.(1$

"! )

,0)-!

,1=*-

, = *-, -

/,=*- 1, *- /,1=*-

$$+& &x(t) x(t 3) x(2t 3)

1 1 1

20 t 530 t

(a) (b) (c)

3/2 5/20 t

# "#"#"#2

J!!$O

, = *-1, - ,1 - ,1 -

/,10B- ,1=*-

45'( ,-,- !!,-,-

.(*(,-,=16(-.(*(, -

x(2t + 1)x(t)

3 1

1

1/2

(b)(a)

1/220 0t t

"#"#

x(0.5)

A

2T t0

! "#("#

x(2t 3)

1

5/23/20 t

" "3%5#

Chapter-01.p65 11/24/08, 1:51 PM19

#

'$%& !"

'()*% !@

'() ! !

!

*

$+& &

"

&

/",&7

&$%$$

!-! !&

!"""!!##$#%!"""!## &'(!'#'%'(!'#')'(!'*+#,

&-*,)!#'!''./.#!01.#%!02.#!03.#

4 ' *!"""!!##$#%!"""!## &'(!'#'%'(!'#')'(!'*+#'(!'#,!#'!''./.#!01.#%!02.#!0133.#!&'5'*',#

0

0.5

1

0

0.5

1

20 30 40

Time in seconds

Signal

Ma

gn

itu

de

Ma

gn

itu

de

50 60 70 80 9010

0

0.5

1

0

0.5

1

20 30 40

Time in seconds

Signal

50 60 70 80 9010

,"#"#"#$"#"#

Chapter-01.p65 11/24/08, 1:51 PM21

: .

:

!

,@-!,J-@

J

4

44$-$899)4-:$9

( >RROAA9ST,-C

?1))'

1 ASM OAA3AL!9"J1))*

* SLCJLAOA5

056

6*93C!"J($$&

4;:$

( J!

1 ,-I

*

'

2 J

B J

& ,-/!NN3=''

% JO

,-

1

= 1

, = %-

,

-

*

= 1

= *

, = 1-

$ ,-/=13=''

+4>761

( J!

,- ,-/* , - ,-/ )/

,- ,-/1() ,- ,-/())61)) ,- ,-/,- ,- ,-/*6"

1 ,-,-

: ',-/,-6,- ',-

I

8

1

1

-

4

?

Chapter-01.p65 11/24/08, 1:51 PM22

* O

,- ,-,=1- , - ,-,(=- ,- ,*=-,-

,- =1,1=- ,- ,)261- ,- ,-=,=*-

' ,-C((

,- ,!*- , - ,1-

,- ,01- ,- ,!1-

,- ,*!1-

2 CO

,-

, -

,-

B

O

,-)% 3 ) '

, -) 3

, -=1, - () , -

,-( 3 ) '

, -) 3

,- ( *

, -) 3

& !II

,- , - 1 * * '

, -(

, -*

,- 1, - 1 B

% ,-,-!77

: ,-6,-/',- I',-

I

$ . !

,- ), -/

, - ,-/(1

() I

I G

.0

,- ,1==*-,- , - )/

,- ,=1-=,=-- ,- =1,-

,- =2 ,-=

;, (- 0 B!

,- O6/()3)/1)0/0'3/)(()))

, - :O/51:/()03)23

O)(/)G=1R61R

1 VA?>!

,- JO66/B3/=23O)(" O()))3

/()=*

, - LO,-/66/(3/23O)(:/

()))

* JOA?>!,-/6=!6/())3/%3)/()3O)(3:/()))

' VA?>:O

,- ,-:O/)(()#/) ()#

, - ,-V!:O# 1)!

2 :,-/()1

% *

A?>V

stemA?>B'B A?> !

::%

:

x(t)

0 2

1

3 t

+

Chapter-01.p65 11/24/08, 1:51 PM27