When designing an FIR filter it is handy to know how many coefficients are required for your desired implementation.
The Kaiser approximation is the algorithm that tells you how many coefficients your filter will need but not what those coefficients are. It is accurate when using an approximation design algorithm such as the Parks-McClellan (Remez exchange) algorithm.
For designing filters with the windowing functions there are no direct equivalents to Kaiser's approximation, it is more that you have to look at the characteristics of your signal requirements and compare them to the capabilities of the windowing functions. Note : filters designed using windowing functions will typically be longer than those designed using Parks-McClellan.
SigLib includes a range of windows based filter design functions. At the present time it does not include a version of the Parks-McClellan algorithm because there are so many already available. I had a customer recently use this : http://www.iowahills.com/Example%20Code/NewParksMcClellan.txt.
I haven't used this myself but I have heard good reports.
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