Digital Signal Processing Reference
In-Depth Information
1
0.5
0
−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1
(a) Normalized Frequency
1
1
0.5
0.5
0
0
−1
−0.5
0
0.5
1
0
2
4
6
(b) Normalized Frequency
(c) Normalized Frequency
x 10
−3
1
0.5
0
−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1
(d) Normalized Frequency
Figure 3.34:
(a) DTFT magnitude of a cosine wave of length 2ˆ14 and frequency 2000; (b) DTFT
magnitude of a length-2ˆ14 rectangular window having 1001 contiguous, central values of 1.0 with all
other values equal to 0; (c) A zoomed-in view of part of (b); (d) Frequency response of the windowed
cosine sequence, i.e., the magnitude of the circular convolution of the DTFTs at (a) and (b).
Blackman
The
blackman
window of length
N
is computed according to the following formula, in which
M
=
N
-1:
0
.
42
−
[
]+
[
]
=
0
.
5 cos
2
πn/M
0
.
08 cos
4
πn/M
n
0:1:
N
-1
w
[
n
]=
0
otherwise
Let's take a look at the attenuation characteristic of the
blackman
window using a log plot, which
shows the fine structure of the sidelobes. From Fig. 3.38, plot(d), you can readily see that the scalloped
sidelobes are still there, only greatly attenuated relative to the rectangular window's sidelobes. The central
lobe, however, is much wider than that of either of the rectangular or hamming windows.
Kaiser
The
kaiser
window is not a single window, but a family of windows that are specified by the number
of samples in the desired window and a parameter
β
that essentially allows you to choose the tradeoff
between main lobe width and sidelobe amplitude. Figure 3.39 shows the
kaiser
window with
β
=5.
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