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Measurement, Instrumentation, and Sensors Handbook, Second Edition, 2nd Edition
book

Measurement, Instrumentation, and Sensors Handbook, Second Edition, 2nd Edition

by John G. Webster, Halit Eren
February 2014
Intermediate to advanced content levelIntermediate to advanced
1921 pages
82h 13m
English
CRC Press
Content preview from Measurement, Instrumentation, and Sensors Handbook, Second Edition, 2nd Edition
17-6 Electrical Variables
Assuming now that instead of innite terms in the expansion of Equation 17.12 M terms are main-
tained,
th
en
an ap
proximation
of f(x) is su
cceeded
. e ex
pansion
of f(x) us
ing
Eq
uation
17.12 is a
Ga
uss–Hermite
se
ries
. Eq
uation
17.12 is a fo
rm
of Fo
urier
ex
pansion
fo
r
f(x) an
d
ca
n
be co
nsidered
as th
e
Fo
urier
tr
ansform
of f(x) su
bject
on
ly
to a sc
ale
ch
ange
. In
deed,
th
e
Fo
urier
tr
ansform
of f(x) is
gi
ven
by
F s f x e dx f x F s e ds
jsx jsx
( ) ( ) ( ) ( )= =
−∞
+∞
−∞
+∞
1
2
1
2
π π
(1
7
.14
)
e
F
ourier
t
ransform
o
f
t
he
b
asis
f
unction
ψ
k
(x) of Equation 17.8 satises [9]
Ψ
k
k
k
s j s( ) ( )=
ψ
(1
7
.15
)
while
f
or
t
he
b
asis
f
unctions
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Publisher Resources

ISBN: 9781439848913