Next |
Prev |
Up |
Top
|
Index |
JOS Index |
JOS Pubs |
JOS Home |
Search
Given a prescribed side-lobe ripple-magnitude
and main-lobe width
, the required window length
is given by [155]
![$\displaystyle M = 1 + \frac{\cosh^{-1}(1/r)}{\cosh^{-1}[\sec(\omega_c/2)]}.$](img551.png) |
(4.52) |
For
(the typical case), the denominator is close to
, and we have
![$\displaystyle M \approx 1 + \frac{2}{\omega_c}\cosh^{-1}\left(\frac{1}{r}\right)$](img554.png) |
(4.53) |
Thus, half the time-bandwidth product in radians is approximately
![$\displaystyle \beta \isdefs (M-1) \omega_c\approx 2\cosh^{-1}\left(\frac{1}{r}\right),$](img555.png) |
(4.54) |
where
is the parameter often used to design Kaiser windows
(§3.9).
Next |
Prev |
Up |
Top
|
Index |
JOS Index |
JOS Pubs |
JOS Home |
Search
[How to cite this work] [Order a printed hardcopy] [Comment on this page via email]