, L-3 PROPERTIES OF THE FOURIER TR ANSFORM IIIMMINED a G (4.) = - - PowerPoint PPT Presentation

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EE 308 / Slide

L-5

PROPERTIES OF THE FOURIER TRANSFORM

• NINAI■•••

CDEEP IIT Bombay

EE 308 / Slide

1,

PROPERTIES OF THE FOURIER TR ANSFORM

■IIIMMINED

a G (4.) = Sg(t)exp(- j1nf t) dt

9 (t) =

S

co

&Mel+ (

327r4t)d+

_op

• 9(t)

CiG)

FT ?CO

G4)

eies(fil

iG-(4)\

continuous 'coviptitude spectrum

(3(t)

( 9(4)

continuous phase spectrum'

04 g(t)

For the s?ecial. case 64 o real-valued wcrt• 96E)

i•e'l

'G(-4)1 1:-

' \ GC41\ --pp even-in.

$

61(4) = -- Gs(4) .-a, odd 4vt.

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EE 308

/

Slide 2.

L-3

i.e•,

EXAMPLE:

colurie symmetry

Recton9ulav Pulse (Box Function)

2

2.

0 .t

< 4 OR

2

vect (t)

i

• k.

i.

2

9(0= A red ( t )

• r

Sk)

A

CDEEP IIT Bombay

EE 308 / Slide

3

L.•3

• G. (.0

* -1.

• 2. 2.

= (1 12.

. A, vx,\) t.:11114t)

it

) A elq C.:3214-.0dt

• 112

.:1 2.14

'l

s i

~ c (41"

..

. soft

(lot)

gni*

• r. pi,
• -'32.14

e:111) ...:1ER 41) -- ell) VIIS41)

• K-f-

AT sinc,(4.7)

AT

• Ayr
• spr
• 21T
• 7T

Yr

2,

3 Ar

crm

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/

Slide 4

L-3

(%) 1.,..ih•orstv Cs44113ossrifoh)

so) *--ip G k(f)

7

to< i_sk(so 4

....._„•• "2 giA(41

lk

4

rk

(2) .,. II- kenow

(rnytie Set:dais)

v5 (4) *--P CT(*)

Z Ca0 4---s~~

.1.. Gs (-1

lal

6

4

SW 4--ap 6(4)

Sik (k)ec---P G*

(4 )

(3) CovNjuga-hoh

Useitsa ?r

roes 0 ktf~e Runty Ininsimi

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EE 308 L7_3_ /

Slide_a___

( 10

ualiity

Es:

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EE 308 L I I Slide_e__

Vaik A sivic (Iwt)

sct)

ik

w

y.4 w i

tw

Asty,c, (2V4t) *-----* )14"44.11,4) 2A (2-

1C;4)

Akw

1

4W

CDEEP IIT Bombay

EE 308 L 3 /

(5) Ti

me StAi4gilti

5(+)*--ar G(4)

S(tAtv)

Vilf) elt1:$ (•-jansF•iyo)

(6) F-Yeve

V% Cy

Sit%

sc+14.-A,G6fri ep-xl) C) 27refet)g(t)

G (+4, )

11)

Avea wideit 9 CIO

Area uhdefr G(f)

Sc%(f)df

• -co

(S )

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EE 308 L 3 / Slide

(4) .3) inc•fe revsubia rt in "T'i *le 7%40 metal 9 (-0 e-ar G (4 )

g

wit

'lv,

• )ple

2,..

t.

..errt .or-f

le

fl---P e

(to)

3h4t5re~ lion Iry 46e Time ,oivitui:v i, 9 Cet) 4--, ~G(f)

st5,10, e......

G(+1 + J. 6-(o)SCac)

• 0 ei

274

2

M 0 dtA Id410

"Th e 0 Ple144

9 1 (t) sim'W

vo

4—kr Ga

(it) Covweltehort

sillworeoi

91,(104-1,

(+)

SI,

("0 91.(-twat) sti er rs G, (fJGs6t)

g CO 9,(0 4—p

Cc, 4) k

(efw )01A

CT1 (f) Gs4)

CDEEP IIT Bombay

EE 308 L 3 / Slide

CDEEP IIT Bombay

EE 308 L 3 / Slide

10

EFTA

FUNCTION

(et) =o f to

45°D

dlOoiat =

• -co

OQ

9 (Joe (et-

6)cif = 3 Cto) Seftuig

to iippevN

d7t)

c_c ) cis (t-r)

(t) 80) * citt) = 5 •b

)

Re

9v9i)et