[LAD] Is this sort of window function used? (can't identify)

While experimenting with window functions for spectral analyzis, I
compared Hann, Sin and Lanczos. It is easy to notice, that Hann is
really same as sin(x)^2. Lanczos is tiny bit better, because its sides
are tiny bit smoother, compared to sin(). It seems, that unsmoothed
corners between sides and zero axis for sin() is reason why sides are
so high, compared to Hann. Hamming and more over Gaussian have ideal
smooth sides, but narrower middle (probably this one reason why central
leaf is wider for them).

Just for experiment i tried to change sin(x)^2 to just sin(x)^f, where
1.0f < f < 2.0f. And it looks like any f>1 causes derivative to be =0
at zero axis. The only thing, affected by exact amount in this range,
is how fast it will become zero. While it is easy to notice with Hann
example, factor around 1.2 or 1.1 make it hard to notice without very
deep zoom. With f=1.25 or 1.26 it nearly reproduces Lanczos, thought
difference may be noticed, if plotted at the same time.
Though still not have enough precise integral for weakening correction,
i noticed that side leafs falldown slightly faster than for Hann.

Now I'm curious, is such function is in use? I don't know how to call
it for search request. E.g., after reinventing Welch window by just
multiplicating y=2x with y=2-2x, I already knew it is parabola. For
sin(x)/x i know it is sinc. But what is sin(x)^y, at least at some
'y' between 1 and 2 ?

I feel, that this is also something reinvented. Just like writing
sin(x)^2, i discovered later that it is Hann. Need help.

One of professors, who are still aware of signal processing stuff,
adviced me to reed this book (found localized to russian):
https://www.scirp.org/(S(351jmbntvnsjt1aadkposzje))/reference/ReferencesPapers.aspx?ReferenceID=34577

but i still have to find time to learn it (besides of deepening my
math knowledge).
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Received on Mon Apr 15 16:15:01 2019