Biomedical Engineering Reference
In-Depth Information
parameter, and according to this value we have a family of windows. The usual value of
alpha is 0.10 or “10% Tukey Window” (often called a ten percent window) [1]. Another
name for the family of these windows is cosine-tapered windows. The main idea behind
any window is to smoothly set the data to zero at the boundaries, and yet minimize
the reduction of the process gain of the windowed transform. There are several Tukey
windows for different values of alpha ranging from 0.10 to 0.75.
The mathematical model for the ten percent Tukey window is given by equations
in (16.3). Since the formula is taken from our signal processing program, the variable
“alpha” has a value of 0.10.
5
1
cos
10
π
i
w
(
i
)
=
0
.
−
for
i
=
00 to 0
.
1
N
10
w
(
i
)
=
1
for
i
between
i
=
0
.
1
N
to 0
.
9
N
(16.3)
5
1
cos
10
π
i
w
(
i
)
=
0
.
−
for
i
=
0
.
9
N
to
N
10
Notice that for the last and first ten percent of data the window function is the
same. Higher alpha values tend to increase the main lobe spread with less leakage results.
For an alpha of 0.10, the Tukey window has the first side-lobe level at
−
14 dB with
a roll-off rate of
18 dB. It is interesting that the first side-lobe level and the roll-off
rate characteristics remain the same for alpha values up to 0.25. The Tukey window
time domain weighted coefficients for alpha values of 0.25, 0.5, and 0.75 are shown in
Figs. 16.8(a), 16.9(a), and 16.10(a), respectively. The resulting Log-magnitude of the
Fourier transform for alpha values of 0.25, 0.5, and 0.75 are shown in Figs. 16.8(b),
16.9(b), and 16.10(b), respectively [1] and [2].
−
16.3.5 Hanning Windows
The Hanning family of windows is also known as the “Cosine Windows,” since the func-
tions used are true cosines. For the readers, historical information, the name “Hanning”
does not exist, since the founder of these functions was an Austrian meteorologist named
“Hann.” The
ing
ending was added because of the popularity of the cosine window mod-
els. The mathematical model for the Hanning window is given by equations in (16.4).
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