[PD] Window Functions

[Miller Puckette]

There are many variations on this.  The main difference is a slight
phase change - which, on reconstructing the signal, might give one more or
fewer sample of delay.  Other than the phase difference the effect is
very small since the values at teh tails are on the order of N^(-2) (one
over a million for N=1024).

cheers
Miller

On Sat, Jan 09, 2016 at 12:08:02PM -0500, Matt Barber wrote:
> Excellent, thanks. One reason I'm wondering is that many definitions of
> window functions in DSP texts and online define Hann as something like
> 0.5*(1 - cos((2*pi*n)/(N - 1))), which is the symmetric version, 0 at both
> ends. With overlap-add it puts a repeated value at both peak and trough,
> but still with the FFT periodicity.
> 
> On Sat, Jan 9, 2016 at 7:02 AM, katja <katjavetter at gmail.com> wrote:
> 
> > Hi Matt,
> >
> > What I remember from FFT experiments is, a 'periodic' Hann window
> > (asymmetric) gives best results for overlap-add. You can think of the
> > window as two functions: the DC component preserves the original
> > signal, while the cosine component produces sum- and difference
> > frequencies which cancel each other in subsequent overlaps after IFFT.
> > Long story and illustrations here:
> >
> > http://www.katjaas.nl/FFTwindow/FFTwindow&filtering.html
> >
> > Katja
> >
> >
> > On Sat, Jan 9, 2016 at 6:39 AM, Matt Barber <brbrofsvl at gmail.com> wrote:
> > > Hi list, quick DSP question.
> > >
> > > In I02.Hann.window.pd there is a Hann window computed by running an
> > [osc~]
> > > for one cycle over 512 samples. Doing it this way is simple but it means
> > > that it doesn't taper all the way to 0 on the right (the next value of
> > the
> > > oscillator after writing the table is 0). I don't know why I hadn't
> > thought
> > > of this before, but is this asymmetry mathematically optimal for
> > windowing
> > > of a single frame? What about in an overlap-add context? I'm trying to
> > > understand the logic, so I'm not too worried about whether it makes a
> > > practical difference. A period of 511 samples would be symmetric and
> > > 0-valued at both ends, but there would be no "middle" value at unity.
> > >
> > > What's the best way to think of this?
> > >
> > > Matt
> > >
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> >

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