Biomedical Engineering Reference
In-Depth Information
FIGURE 2.15:
STFT as atomic decomposition. A sliding window (thick line) ex-
tracts a portion of signal roughly localized in time. This windowed signal is “com-
pared” with each of the time frequency atoms of the form
h
t
,
f
e
i
2π
fu
,
(
u
)=
h
(
u
−
t
)
giving the Fourier components (
h
t
,
f
(
u
)
weighted by intensities).
2.4.2.2.2
Continuous
wavelet
transform
and
scalogram
The
continuous
wavelet transform (CWT) is defined as
Z
∞
Ψ
t
,
a
(
T
x
(
t
,
a
;Ψ
)=
x
(
s
)
s
)
ds
(2.91)
−
∞
where Ψ
t
,
a
is obtained from the mother wavelet Ψ by time translation
t
and dila-
tionbyscale
a
:
(
s
)
Ψ
s
1
−
t
(
)=
Ψ
t
,
a
s
(2.92)
a
|
a
|
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