[sdiy] Harmonic bandwidth

[ASSI]

On Sonntag 06 Januar 2008, Tom Wiltshire wrote:
> What I was most interested in was the use of IFFT to get from a non-
> perfect harmonic spectrum with spread harmonics (and even noisy
> smearing at the high end) to a loopable sample that can be used for a
> wavetable. This seems like a good idea.

No. OK it seems like a good idea, but actually isn't.  Sorry, I'm not 
trying to mock you, but this is a pitfall that has claimed many victims 
in the past and seemingly will eternally.  If a sample is looped, it 
becomes periodic and you get a discrete spectrum by definition.  You 
get more discrete spectral lines as the sample gets longer, but they 
are still discrete.  The concept of spread harmonics in this context is 
pretty dubious in many ways.  If you forego the periodicity requirement 
at the base of the definition of frequency entirely and start to define 
frequency content in terms of energy transfer into narrow-band filters 
of varying bandwidth then you might get somewhere (specfifcally you'd 
perhaps be able to match this notion with the physiological mechanism 
of human hearing).

> Building a waveform up from 
> (say) 50 perfect sine waves at perfect integer multiples is never
> going to give a natural-sounding wave.

I contest there even is such a thing as a natural sounding wave.  A wave 
is a one-dimensional thing and nature sure isn't.

> At first, I thought this would be the same as simply using many
> detuned oscillators, since if an oscillator is detuned by (say) 1Hz,
> then its 2nd harmonic is detuned by 2Hz, and the 3rd by 3Hz, etc,
> giving the frequency spread effect that we're after. But this isn't
> quite right. Doing it that way is going to give you as many sinewaves
> at the fundamental (and as much smearing, although not as detuned) as
> at some higher harmonic.

Well, then use less detuned oscillators on the fundamental and more 
detuned oscillators for the higher harmonics.  There is nothing 
especially complicated about it if that's the result you want to see.  
On the other hand you could just use one oscillator for each harmonic 
and modulate that oscillator suitably and arrive at the same result.  
And then you can of course do an IFFT with chosen parameters and get 
the same result again.

> The IFFT technique will give you clearer 
> lower harmonics (with less sines) and more smearing at higher
> frequencies (with many sines). This _does_ mimic what you see if you
> run an FFT on an acoustic instrument.

The smearing you see in an FFT of acoustic instruments has much more to 
do with the limitations of the method itself.  The FFT assumes a signal 
to be periodic ad infinitum and falls down if it actually isn't.  You 
can easily try it out yourself: take a strictly periodic singal and add 
a sligthly detuned version of the same.  Then do an FFT on the result: 
instead of getting two spectral lines for each harmonic you will get 
single, broader peaks which sometimes don't even have the correct 
amplitude and spurious frequency components that are not in the two 
original signals.

That's why better methods have been invented to analyze signals which 
are quasi-periodic or even non-periodic.  For instance you can improve 
frequency resolution at the expense of some other parameters - reading 
up on all of this will easily lock you down in your favourite library 
for a month or drive you mad or both.  If you follow one line of those 
developments you'll end up with granular synthesis for instance.

> I'm interested to know if anyone has tried/knows of an instrument
> that has tried this technique of using IFFT to produce wavetable
> samples. Is this chap alone?

I know ProTools and the Neuron use re-synthesis techniques with some FFT 
routines at their core, but certainly not a stock IFFT.


Achim.
-- 
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