You get me intrigued with this
I actually believe that wavelets are the way to go for such things,
but, besides that anything beyond a Haar wavelet is too complicated for me
(and I just grasp that Haar very superficially of course),
I think one problem is the problem you mentioned - don't do anything
with the bands,
only then you have perfect reconstruction
And what to do you do with the bands to make a pitch shift or to
preserve formants/do some vocoding?
It's not so obvious (to me), my naive idea I mentioned earlier in this
thread was to
do short FFTs on the bands and manipulate the FFTs only
But how? if you time stretch them, I believe the pitch goes down (thats
my intuition only, I am not sure)
and also, these bands alias, since the filters are not brickwall,
and the aliasing is only canceled on reconstruction I believe?
So, yes, very interesting topic, that could lead me astray for another
couple of weeks but without any results I guess
I think as long as I don't fully graps all the properties of the FFT and
phase vocoder I shouldn't start anything new...
Am 09.11.2018 um 22:31 schrieb robert bristow-johnson:
what you're discussing here appears to me to be about perfect
reconstruction in the context of Wavelets and Filter Banks.
there is a theorem that's pretty easy to prove that if you have
complementary high and low filterbanks with a common cutoff at 1/2
Nyquist, you can downsample both high and low-pass filterbank outputs
by a factor of 1/2 and later combine the two down-sampled streams of
samples to get perfect reconstruction of the original. this result is
not guaranteed if you **do** anything to either filter output in the
filterbank.
---------------------------- Original Message ----------------------------
Subject: Re: [music-dsp] 2-point DFT Matrix for subbands Re: FFT for
realtime synthesis?
From: "gm" <g...@voxangelica.net>
Date: Fri, November 9, 2018 4:19 pm
To: music-dsp@music.columbia.edu
--------------------------------------------------------------------------
>
> hm, my application has also WOLA ...
>
> All I find is about up- and downsampling of time sequences and spectra
> of the same length.
>
...
>
> If anyone knows of an easy explanation of down- and up sampling spectra
> it would be much appreciated.
>
> Am 09.11.2018 um 19:16 schrieb Ethan Duni:
> ..
>> The only applications I know of that tolerate time-domain aliasing in
>> transforms are WOLA filter banks - which are explicitly designed to
>> cancel these (severe!) artifacts in the surrounding time-domain
>> processing.
--
r b-j r...@audioimagination.com
"Imagination is more important than knowledge."
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