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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
17-11Nonlinear System Modeling with Invariance to Fourier Transform for Fault Diagnosis
and the corresponding Fourier transform is
Ψ
T T
j t j t
T
T
j t e dt t e dt( ) ( ) ( )
ω ψ ψ
ω ω
= =
−∞
+∞
(1
7
.26
)
Using
a ge
neralization
of Pa
rseval’s
th
eorem,
th
e
av
erage
po
wer
of a re
al-valued
po
wer
sig
nal
ψ
T
(t) is
co
mputed
f
rom
t
he
F
ourier
t
ransform
a
s
P
T
t dt
P
T
j j
T
T
T
T
T T
ψ
ψ
ψ
π
ω ω
=
=
→∞
→∞
−∞
lim | ( )|
lim | ( ) ( )
1
2
1
4
2
or
Ψ Ψ
dd
P
T
j d
T
ω
π
ω ω
ψ
or
=
→∞
−∞
lim | ( )|
1
4
2
Ψ
(1
7
.27
)
e power spectral density of the signal is computed from the Fourier transform as
S
j
T
T
T
ψ
ω
ω
( ) lim
| ( )|
=
→∞
Ψ
2
2
(17.28)
17.4.3 Power Spectrum of Stochastic Signals
e power spectral density is ...
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Publisher Resources

ISBN: 9781439848913