Question

Fourier Transforms • Find the Fourier transform of et if -a<x<a 0 otherwise. • Find the Fourier transform of S f(0) = 3 10 if - 1<x<1 otherwise
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Answer 1

he Fourier transform of a function f(x) is traditionally densted by f(s). There are several common conventions for defining tourier transform, one of them is Î (8) = so f(x) e striks f(x) = 2 et if- a <xla o otherwise The fourier transform of fre) is given by } (5) = 9 froe mix dx . -21LXS - 200X9 = 5 free mixes dx + 5 few ewis de & froe &x x3 dx 2 e x - 2tics. AL tixsdx to 1 1 1-ztis (1-21) -j-avis) [ 29-asis) a - z mig)(a)? . § (5) = 1 ellaris) a ė (1-2mig)a į (1-21

Here f(x) = 21x1 if L221 o therwise .. § (5) = 5 free vist dx em sua 3 'dx t erwè zitting, + - ots' ixte zrixs akto Sie miksix +5'2sx - - - - - - Hì 4 - 2 attixe o р ம Sxezrixe ax - x. Je Hike & & & & (x). Je zrix dx} dx - xie 2x - je - x.ĕ 271 xq --tię και 2πίχε de J - 2trig - ating - attig zwię 1.763) = * *mo-}" clave Jx L -2tig s-1 znię (2Hig) 2 4e 2015 yang berisia} + camis) = (ant932 + zmes pettis euis) - 2018 pe emis} - 2 + zig zi.sin(293) - ettegiz 2. Cos (248) - 1 2 + 7 sin (218) + 1 coz (208) Hence, (3) = baitz 3 cos (218) -1} + tę Sin (213) 1 13