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The Fourier transform

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hello, in this document i have covered basics and fundamentals of fourier trnaform and the mathemical or numerical based approach is there. those who are preparing for exams this is the best module as it covers all the transformation and formulae it helps ,enjoy learning thank you.

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FoURER TRANS foRM
mathematcalL kval ued fer
towur thanstonm
analyisk gnels
0 Agskim
o)
eol to amulyi
Lplau Aansfon amel Curu k .


Lxut on
foww' tnanfonm
naks
Enera
Poww S nas
Antegro-Bl)

nal Absolutely
mpulse ulakia
Non E S P).

LT 1) ES
Ps
extent).
3) NENP only u

Repnesentakion - t) xjw) on x 4H
) .z
Maalsec

x (jo) =(l xjo)) 2x tjo)

formulaL
5) Lt) x yw)
Jwt

x Lj) Ct).e dt FT
FT
paLn
x jw) x)
valda fobo
t xljt.eJwt
absoute ntegrab 2 7 TF. T
-
ma


on L T to fT




Londit ions fon tstenu towuer seuts Transfarm

Diuchlet's to nelkton ).

,Sugnalsshomo ula hav hinu'tu no. A maximma Amdl
TMimima
ovr Omy cte Antevval
o cus tomtinuitin
sig ma should hav tnite umbu


imtevval.


6 mal hould B asolutely nteg rable
Pooersiqnal (x) may txiat
NENP C)

Th Omaiono mu'ant But net necess any



Popeai of fouwuer Transtovm-

) untaviiy a X,j»)
X C4) X, j»)


BX w)



L4) Xyw)
x tyo) .e dt




DO




+ B Ue dt

X, jo) Yjw)


u poVad

Conyug a k o n
Lt) X Go)
4) x*(-i)
pueef ot) xo)

, jo) = t ) ee


wt
x* Cjo)= ). e dlt




x*juo)= Ct).e ot




L x*lj)
Hmu, phoved.



Am undey a ltt) :

ur ilt) xt) d
-NCot
x jo) ).e dt




X Co)
C4) dt wdey t)



4 ua umdey x fo):
p umde xyu) =xuto) dw

Jot
xjo). e duo
-




Lo)=E x Cjo) d w

2 7 o) |x Lw) d under

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Uploaded on
September 1, 2022
Number of pages
19
Written in
2021/2022
Type
Class notes
Professor(s)
Sujjet singh
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