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Phase Estimation in Optical Interferometry
book

Phase Estimation in Optical Interferometry

by Pramod Rastogi, Erwin Hack
November 2014
Intermediate to advanced content levelIntermediate to advanced
366 pages
11h 5m
English
CRC Press
Content preview from Phase Estimation in Optical Interferometry
94 Lionel R. Watkins
so that the CWT of Equation (3.6) can be written as a convolution integral:
−∞
(,)()(
).Wa
bftbtdt
fa
(3.35b)
Hence, by the properties of the Fourier transform,
F
ψω
{(,)}
ˆ
()
ˆ
()
.Wabf
fa
(3.35c)
Because
ψωω
ˆ
()
ˆ
()
,
aa
a
(3.35d)
the CWT is readily calculated from the inverse FFT according to
F
ψω
−∗
(,){
ˆ
()
ˆ
()
}
1
Wa
ba
fa
f
(3.35e)
=
π
ωψ
ωω
−∞
∗ω
2
ˆ
()
ˆ
()
e.
a
fad
ib
(3.35f)
If we intend to implement the CWT using a FFT, then the data will obvi-
ously be sampled, and we should write Equation (3.35f) as [16]
ψω ω
=
(,)
ˆ
()
ˆ
()exp( )
0
1
Wa
bafa
ib
f
k
N
kk k
(3.36a)
where
=
π
π
>
2
2
2
2
w
k
N
k
N
k
N
k
N
k
(3.36b)
and we have assumed unit sampling interv ...
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Publisher Resources

ISBN: 9781466598317