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/ReferencesPap… > > but i still have to find time to learn it (besides of deepening my > math knowledge).