
17-6 Electrical Variables
Assuming now that instead of innite 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 satises [9]
k
k
k
s j s( ) ( )=
ψ
(1
7
.15
)
while
f
or
t
he
b
asis
f
unctions