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

that's a perfect question for music-dsp (list and archive, start at
https://www.musicdsp.org)...
                                                                ...Diemo

On 15/04/19 13:51, Nikita Zlobin wrote:
> 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).

-- 
Diemo Schwarz, PhD -- http://diemo.concatenative.net
Sound–Music–Movement Interaction Team -- http://ismm.ircam.fr
IRCAM - Centre Pompidou -- 1, place Igor-Stravinsky, 75004 Paris, France
Phone +33-1-4478-4879 -- Fax +33-1-4478-1540
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