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

[Nikita Zlobin]

On Mon, 15 Apr 2019 16:25:06 +0200
Diemo Schwarz <Diemo.Schwarz at ircam.fr> wrote:

> 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).  

I just found, that I erroneously wrote x*pow(x, e), thus automatically
incrementing total exponent (and also why weakening coefficient did not
match). With e=1..2 it just balances between sine and hann
(so essentially :) ).