Geology Reference
In-Depth Information
1.0
-
T
/2
0
T
/2
t
Figure 2.8 The triangular Bartlett window
Δ
(
t
).
the
Bartlett window
, shown in Figure 2.8. The Fourier transform of the Bartlett
window is
∞
−∞
Δ
(
t
)
e
−
i
2π
ft
dt
1
e
−
i
2π
ft
dt
1
e
−
i
2π
ft
dt
0
T
/2
2
t
T
2
t
T
=
+
+
−
−
T
/2
0
T
/2
4
T
=
T
sinc(π
fT
)
−
t
cos(2π
ft
)
dt
0
T
2
sin(
π
fT
)
1
(2π
f
)
2
cos(π
fT
)
4
T
1
=
T
sinc(π
fT
)
−
4π
fT
+
−
(π
fT
)
2
1
2sin
2
π
fT
2
(π
fT
)
2
1
cos(π
fT
)
T
T
=
−
=
−
1
+
sinc
π
fT
2
2
T
2
=
.
(2.280)
The Bartlett frequency window,
the Fourier transform of
Δ
(
t
),
is shown in
Figure 2.9. The height of the
n
th sidelobe is approximately
T
2
·
1
2
T
1)/2
T
)
2
=
2
,
n
=
1,2,3,....
(2.281)
1)
2
(
T
·
π(2
n
+
(2
n
+
π
Although the main lobe is twice as wide as that of the frequency window of the
boxcar, shown in Figure 2.6, the height of the first sidelobe of the Bartlett frequency
Search WWH ::
Custom Search