of Microprocessors

SOURCE-SIGNAL ANALYSIS 563
o
-5
-10
-15
~ -20
:; -25
Cl
::>
!::: -30
-'
c..
~ -35
-40
-45
-50
-55
- 60 '----------'L...Jl""-----,-'-,------'-----L_"'------"------'-'-----"------'JL-J;L---il_l+L-----l1..-.J...........
o 468 624 780 936 1,092 1,248
FREQUENCY (Hz)
(E)
Fig. 16-11. Equivalent half-bandpass filter shapes of common windows (cant.).
(E) Hammingwindaws. HM(X) = 0.54 - 0.46 (COS(21TX)), 0 ~ X ~ 1.
Some Example Windows
Now that they can be easily plotted, let's evaluate some windows.
Perhaps the simplest is a linear rise and fall, which is called a triangular
window. This window, along with the upper half of its equivalent bandpass
response shape, is plotted in Fig. 16-11B. Two characteristics are immediatelyapparent.
First, the leakage attenuation is much better than that of the
rectangular window shown for l'eference. Second, the apparent width of the
central lobe, which is the primary bandpass response, is double that of the
rectangular window. This is the price that is paid for low leakage, and the
lower the leakage, the broader the bandpass. Thus, one must decide how
much leakage can be tolerated and choose a window that meets but does not
greatly exceed that figure. For our example, a figure of -40 dB will be chosen
and none of the secondary lobes, even the one closest to the center lobe, will
be allowed to exceed it. According to this criterion, the triangular window is
not suitable, since the first sidelobe is at -27 dB. Nevertheless, the third
and higher sidelobes are less than -40 dB, a figure that seemingly even the
lOath lobe of the rectangular window cannot meet.
A similar window is the half sine wave. It has the advantage of a flat
rather than pointed top. Its characteristics are shown in Fig. 16-11C. Its
central lobe is only 1. 5 times as wide as the rectangular window, yet has even
better sidelobe attenuation (beyond the first) than the triangular window. Its
second sidelobe, which is at the same frequency as the first triangular window
sidelobe, is about -32 dB.