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@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@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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