In this section, we will learn to find FT of some
basic functions. Fourier transform properties are used in certain cases.
(1) x(t)=e-atu(t) , a>0
By definition,
(2) x(t)=eatu(-t) , a>0
By definition,
Using time reversal property
of fourier transform is another method to solve.
(3) x(t)=e-a|t| , a>0
By definition,
(4) Fourier transform of unit Impulse function
x(t)= δ(t)
By definition,
(5) Fourier transform of
rect function
(6) Fourier transform of
signum function
X(t)=Sgn(t)
Sgn(t) = 1 , t>0
= -1 , t<0
By definition,
(7) Fourier transform of
unit step function
x(t)=u(t)
(8) x(t)=1
Using duality property of fourier transform.
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