Example 7.8.20 Find the Fourier cosine transform of
,for01
()2,for12
0,for2
xx
fxxx
x
<<
⎧
⎪
=−<<
⎨
⎪
>
⎩
.
[JNTU2002, 2003S, 2004S]
Solution The Fourier cosine transform of f (x) is given by
0
12
012
!
2
0
2
2
1
2
2
{()}()()cos
cos(2)cos0.
sin
cos
sincos
(2)(1)
1sin0
1
(coscos0)
(0sin)(cos2cos)
2coscos21
cc
FfxFsfx sxdx
xsxdxxsxdxdx
sx
sx
x
ss
sxsx
x
ss
s
s
ss
sss
ss
ss
s
∞
∞
==
=+−+
−
⎡⎤
⎛⎞
=−
⎜⎟
⎢⎥
⎝⎠
⎣⎦
−
⎡⎤
⎛⎞
+−−−
⎜⎟
⎢⎥
⎝⎠
⎣⎦
⋅−
=+−
−−
+−
−−
=
∫
∫∫∫
2
Example 7.8.21 Find the Fourier cosine transfor ...
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