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

CDEEP IIT Bombay EE 308 / Slide L-5 PROPERTIES OF THE FOURIER TRANSFORM NINAI ■ ••• � , L-3

PROPERTIES OF THE FOURIER TR ANSFORM ■ IIIMMINED a G (4.) = Sg(t)exp(- j1nf t) dt CDEEP IIT Bombay co 1, S EE 308 / Slide • � 9 (t) = � &Mel+ ( 327r4t)d+ 6 _op • 9(t) � CiG) FT ?CO G4) � eie s (fil continuous 'coviptitude spectrum iG-(4)\ � (3(t) ( 9 (4) � continuous phase spectrum' 04 g(t)

For the s?ecial. case 64 o real-valued wcrt• 96E) CDEEP IIT Bombay 'G(-4)1 1:- ' \ GC41\ --pp even-in. i•e'l � $ � Slide 2. EE 308 / L-3 6 1 (4) = -- G s(4) .-a, odd 4vt. i.e•, colurie symmetry EXAMPLE: Recton9ulav Pulse (Box Function) 2. 2 � -k. i. 0 .t < 4 OR vect (t) 2 2 i

9(0= A red ( t ) - r Sk) CDEEP A IIT Bombay 3 EE 308 / Slide L.•3 * - 1. 2 . � 2. . A, vx ,\ ) t.:11114t) = ( 1 12. � it G. (.0 ) A elq C.:3214-.0dt 'l .: 1 2.14 � -112 � r. pi, 11 e:111) ...:1ER 41) -- ell) VIIS41) s i ~ c (41" .. . soft (lot) --'32.14 gni* ..... A sly, ciicol - K-f- AT sinc,(4.7)

crm AT CDEEP IIT Bombay Slide 4 EE 308 / L-3 - Ay r -sp r -21 T -7 T 2 , � 3 Ar Yr

roes 0 ktf ~ e Runty Ininsimi U seitsa ?r 0 (%) 1.,..ih•orstv Cs44113ossrifoh) so) *--ip G k (f) CDEEP IIT Bombay 7 to< i _ sk (so 4 308 L7_3_ / Slide_a___ EE ....._„•• "2 giA(41 rk 4 � lk � (2) .,. II- kenow (rnytie Set:dais) v5 (4) *--P CT(*) .1.. Gs (-1 6 Z Ca0 4---s ~~ lal 4 (3) CovNjuga-hoh SW 4--ap 6(4) (4 ) S ik (k)ec --- P G *

ualiity ( 10 � CDEEP IIT Bombay Es: Vaik A sivic (Iwt) EE 308 L I I Slide_e__ sct) ik y.4 w i t w w A sty , c , (2V4t) *-----* )14"44.11,4) 2A � (2- 1C;4) Akw 1 4W

me StAi4gilti (5) T i 5(+)*--ar G(4) Vilf) elt1:$ (•-jansF•iy o ) S(tAtv) � CDEEP IIT Bombay (6) F - Yeve EE 308 L 3 / V% Cy Sit% sc+14.-A,G6fri ep-xl) C) 27 refet)g(t) � G (+4, ) Avea wideit 9 CIO 11) . S ° S (-0 Gilt = G(o) Area uhdefr G(f) (S ) S c %(f)df --co

(4) .3) inc•fe revsubia rt in "T'i *le 7%40 metal 9 (-0 e-ar G (4 ) wit CDEEP g 'l v, IIT Bombay EE 308 L 3 / Slide � � )ple � 2,.. t. ..errt � .or-f fl --- P e le � 3h4t5re ~ lion Iry 46e Time ,oivitui:v i, 9 Cet) 4--, ~ G(f) (to) st 5,10, e...... G(+1 + J. 6-(o)SCac) -0 � e i 274 � 2

"Th e 0 Ple144 M 0 dtA Id410 � 9 1 (t) sim'W vo 4—kr Ga CDEEP IIT Bombay g CO 9,(0 4—p (efw )01A Cc, 4) k EE 308 L 3 / Slide CT1 (f) Gs4) si llworeoi (it) Covweltehort 9 1 ,(104-1 , (+) SI , ("0 9 1 .(-twat) sti er rs G, (fJG s 6t)

FUNCTION EFTA (et) =o f to CDEEP 4 5 °D IIT Bombay 10 EE 308 L 3 dlOoiat = / Slide •-co OQ to iippevN Seftui g 6 )cif = 3 Cto) � 9 (Joe (et- d7t) c _ c ) c is (t-r) � (t) Re � 80) * citt) = 5 •b 0 ) 9 v9i)et