Talk:Kaiser window

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Contents 1 Window Center 2 Nearly Optimal 3 Frequency spectra 4 "Off-by-one error"

[edit] Window Center

There is a discrepancy between here and http://en.wikipedia.org/wiki/Window_function#Kaiser_windows on the expression of Kaiser window. I found this while implementing some C++ code. This page's expression centers the peak at 0 while the other page is at N/2. As a newbie on DSP I hesitate to make the change but I did find it confusing, especially since this page mentions that the window is centered at N/2. Rud 18:17, 28 September 2006 (UTC)

My own comparison of the two expressions concludes that the other one spans [0,N-1], whose center is (N-1)/2, which is a little different than your observation. And this one spans [0,N], whose center is N/2, not 0. The two expressions are not different enough to behave as you say, so I advise you to check your code again. --Bob K 19:14, 28 September 2006 (UTC)

Specifically, check for this mistake (note the missing "1" term):

--Bob K 19:23, 28 September 2006 (UTC)

Or more likely you put it in the wrong place, like this:

What you want is this:

--Bob K 19:29, 28 September 2006 (UTC)

[edit] Nearly Optimal

In what sense is the Kaiser window a "nearly optimal window function"? What does that mean? --Bob K 16:18, 12 December 2005 (UTC)

From Oppenheim, Schafer, and Buck:

The trade-off between the main-lobe width and side-lobe area can be quantified by seeking the window function that is maximally concentrated around ω=0 in the frequency domain. The issue was considered in depth in a series of classic papers by Slepian et al. (1961). The solution found in this work involves prolate spheroidal wave functions, which are difficult to compute and therefore unattractive for filter design. However, Kaiser (1966, 1974) found that a near-optimal window could be formed using the zeroth-order modified Bessel function of the first kind, a function that is much easier to compute.

Unfortunately, Oppenheim et al. is not very precise in defining what is meant by "maximally concentrated"; presumably it is in the references. Anyway, this is the sense in which that book calls it "near-optimal". If you have a chance to look up a more detailed explanation, that would be a nice addition to the article. —Steven G. Johnson 20:09, 12 December 2005 (UTC)

[edit] Frequency spectra

I replaced the frequency spectra plots by Bob K (old ones were Image:Kaiser_window_function_alpha_2.png and Image:Kaiser_window_function_alpha_3.png). I found the old ones hard to read because of the plotting format that was used — all sorts of Moire effects, etc. Also, it is nice to keep the same format as the time-domain plots we already have, in particular putting two α values on the same plot so that you can directly compare their spectra, and using a similar color and labelling scheme. (On the other hand, Bob's side-by-side plots look very nice in the context of the Window function article.) —Steven G. Johnson 22:19, 15 December 2005 (UTC)

Yours is definitely a better treatment of the "grass". All I can say in my defense is that in all my years of using window functions, no-one ever cared what the grass looks like below the peaks. And your overlay is essential to compare the lobe widths. I might have picked bolder colors, but good job! --Bob K 23:31, 15 December 2005 (UTC)

[edit] "Off-by-one error"

Not surprisingly, the strength of Wikipedia is also its glaring weakness... it takes constant vigilance to prevent erosion. Hopefully someday there will be a better way, but I don't know what it is. Thoughts? --Bob K 11:21, 7 May 2006 (UTC)

Wikipedia:Stable versions is one proposal to address this. Time will tell whether this works in practice. —Steven G. Johnson 17:49, 7 May 2006 (UTC)

Thanks. It's a start, at least. One thing I do not understand from that proposal is how one will know that a stable version exists? --Bob K 13:57, 8 May 2006 (UTC)