UploadFile_6417

Window Design Techniques 331
where I 0 [ · ]isthemodified zero-order Bessel function given by
∞∑
[ ] (x/2)
k 2
I 0 (x) =1+
k!
k=0
which is positive for all real values of x. The parameter β controls the
minimum stopband attenuation A s and can be chosen to yield different
transition widths for near-optimum A s . This window can provide different
transition widths for the same M, which is something other fixed windows
lack. For example,
• if β =5.658, then the transition width is equal to 7.8π/M, and the
minimum stopband attenuation is equal to 60 dB. This is shown in
Figure 7.15.
• if β =4.538, then the transition width is equal to 5.8π/M, and the
minimum stopband attenuation is equal to 50 dB.
Hence the performance of this window is comparable to that of the
Hamming window. In addition, the Kaiser window provides flexible transition
bandwidths. Due to the complexity involved in the Bessel functions,
the design equations for this window are not easy to derive. Fortunately,
Kaiser has developed empirical design equations, which we provide here
Kaiser Window : M=45
Amplitude Response in dB
1
0
w(n)
Decibels
42
0
22.6383
−22 0 22
n
Amplitude Response
−1 0 1
frequency in π units
Accumulated Amplitude Response
0
Width=(7.8)*pi/M
Wr
Decibels
60
0
0 22 45
frequency in π units
−1 1
frequency in π units
FIGURE 7.15 Kaiser window: M =45, β =5.658
Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.