# [PD] how does env~ work?

Orm Finnendahl orm.finnendahl at selma.hfmdk-frankfurt.de
Fri Mar 24 10:13:45 CET 2017

```Am Donnerstag, den 23. März 2017 um 17:00:14 Uhr (-0300) schrieb Alexandre Torres Porres:
> > the hanning envelope itself actually goes from 0 to "2" and not from 0 to
> > 1, so I assume the compensation is done right there...
> >
>
> tested with an envelope going from 0 to 1 and lost about 3.0103 dB ;)

You're almost there: If you average the values in a rectangular window
with the amplitude 1 you will get 1, the same value results if
averaging the values of a Hanning window with amplitude 2 (you can
check that by building the definite integral of the Hanning function
cos(x-pi)+1 in the interval [0..6.28] and divide that by the width of
the interval (6.28)).

If you use a Hanning window of amplitude 1, you'll get 0.5 as the
average. As the windowing is applied to the squared values, after
calculating the root (for obtaining the "R"MS), you'll end up with
sqrt(0.5) = 0.707 of the "real" RMS value and that equals to -3.0103
dB.

In short: Using a Hanning window with amplitude 2 on the squared
values will compensate the loss of the resulting mean value introduced
by the windowing function. The result is a compensated RMS value with
an emphasis on the center of the analysis window. In this use case the
windowing results in smoothing the irregularities you observed when
using rectangular windows.

--
Orm

```