MOTM

I'm well aware of the windowing problem.  The greater the number of samples 
the more accurate the FFT in terms of determining frequencies but only if 
the frequencies are constant which is not always the case.  With fewer 
samples and a smaller window the time varying amplitude of the harmonics 
could possibly be determined more accurately, but at the expense of 
frequency accuracy.  It may be possible to use a combination of large and 
small windows to get the best accuracy, but there will still be errors.

I read a paper online where someone was proposing improving FFT analysis 
accuracy by first performing an FFT on a sample, then using the inverse FFT 
to resynthesize the original signal (both frequency and phase information) 
then adding the inverted resynthesis waveform to the original to cancel out 
everything but the error.  Then you could conceivably analyze the error. 
 Possibly the error signal could be synthesized using a different method 
than Fourier.

It is possible that the amount of data is simply overwhelming.  I do not 
know for instance how many data points are required for each harmonic 
envelope, whether or not phase accuracy must be maintained, or how 
complicated the algorithm has to be defining the behavior of the harmonics 
(and their envelopes) over the range of a given instrument.

The problem with using filters is that (if I remember my Math and EE 
correctly) the narrower the filter the more it tends to ring, thus 
impairing analysis.  Phase response is not maintained when passing a signal 
through most filters, except the digital FIR (fixed impulse response) 
variety.  Most filters of the type we commonly think of tend to smear the 
sound due to differing phase shifts for different harmonics.  It may be 
possible to overcome this problem by using some sort of swept heterodyning 
method.

Other ideas for possible analysis would probably include using the Walsh 
transform, but generating and analyzing sounds using this method is not 
intuitive.  It also might be possible to use some sort of inverse Bessel 
function and determine synthesis parameters using FM as was done on the 
DX7, but this would require VCOs or DCOs which can be frequency modulated 
through zero.

The whole point (at least as far as I'm concerned) is to try to become 
better educated as to why things sound as they do.  If it using FFT 
analysis leads to better synthesis so much the better.  The ear/brain uses 
a sort of FFT, and interestingly enough it appears now that the ear is 
actually digital, not analog, but that's another issue.  Since we hear by 
sort of a Fourier analysis, that makes the most sense when trying to do an 
analysis.  In theory you can synthesize any periodic waveform with a series 
of sine waves, given enough control over frequency, phase and amplitude.

-----Original Message-----
From:	Tobias Enhus [SMTP:tobias@...]
Sent:	Sunday, June 15, 2003 10:04 PM
To:	motm@yahoogroups.com
Subject:	Re: [motm] Re: file uploaded, Additive Synthesis, Strings, 
Fourier, etc

 << File: ATT00068.htm >> My point exactly, the use of discrete operators 
is the way to go, nice
sounding such too. What I'm talking about is the analysis stage. How to
extract those overtones and their envelopes, with some sort of averaging
function that makes musical sense. A more simplified, pure way. Like you
say, not necessarily to reproduce a natural sound, but a sound that
sounds good.
Even if you play back an FFT analysis through discrete oscillators , you
still get flutter etc.

FFT is probably the way to go in the end, but with a couple of smart
timbral averaging additions.  Then you also need a way to get smooth
envelope curves with only a few points (few compared to unlimited..).
Smooth but without loosing information in the attack.

I've played with the Axcel many times, and I always come to the same
result, nothing....
It's got the coolest user interface on the planet, but the worst
sounding engine ever. Great show piece but nothing more.

T

>
> IIRC those artefacts mostly come from windowing and their inherent
> shifting and overlaping. Which is not the case when descrete
> oscillators (operators) are in play (wether they are in software or
> hardware) but OTOH
>
> How about the Technos Axcel? AFAIK it uses 64 harmonics.
> But IMO it still sounds rather artificial.
> (http://archive.keyboardonline.com/features/vintagegear/vgear0101.shtml)
> 
<http://archive.keyboardonline.com/features/vintagegear/vgear0101.shtml%29>
>
> > How about a more un orthodox way of creating additive spectra's.
> What if
> > you would use a vocoder approach and record the rms for each band.
> > This requires a lot of filters, but it wouldn't have to be real time.
>
> IMHO not efficient enough and maybe (or even for sure) much more
> artifacts than with common FFT methods.
> Probably nice to get "new sounds" (can't hear that term anymore) but
> IMHO not worthwhile the effort.
>
> My point in this discussion is how to obtain more detailed information
> on sounds to bring me closer to desired results. And I'm not
> necessarely after natural sounds as the final result.
>
>     Michael.
>
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