Subject: Re: [linux-audio-dev] Re: chebychev
From: Tim Goetze (tim_AT_quitte.de)
Date: Thu Oct 31 2002 - 23:05:12 EET
Steve Harris wrote:
>On Thu, Oct 31, 2002 at 05:21:08 -0800, Bill Schottstaedt wrote:
>> > there's one problem i see: if we employ a chebyshev, it is going
>> > to create harmonics no matter what amplitude our incoming signal
>> > [...]
>> > it seems hard to come up with a wave shaper that favours higher
>> > harmonics,[...]
>>
>> I have only been skimming this discussion, but these caught my eye,
>> and I'm wondering what you mean by "chebychev" here. If you're
>> driving a sum Chebychev polynomials with the original signal, none of
>> these statements is necessarily correct -- you can preload a table
>> with the polynomials, so the computational load can be unrelated to the
>> harmonic content; the content will depend on the input amplitude; high
>> harmonics are easy -- just emphasize the relevant polynomial --
>> probably I don't know what you're talking about.
>
>No, we are talking about the same thing, but the computational cost of
>evaluating the chebychev depends on the order of the polynomial and
>therefore the number of harmincs you want to generate.
and we need quite a few. i've created an image of the spectral
evolution of an ~500 Hz sine from inaudible to full distortion:
http://quitte.de/spectral-evolution.gif
as you can see, the spectral content changes significantly with
the amplitude of the signal; this may well be what makes this
kind of distortion sound interesting.
looking at the above plot, i more and more think that the chebyshev
may well be the way to go. i don't think any combination of filtering,
exp()- and sine()-based shaping will produce anything like this; if
this can be modeled without employing the chebyshev, my feeling is
that a suitable shaper would need to be based on a more accurate
model of what's happening inside the amp.
the table idea sounds convincing, however there's still the problem of
how to blend between polynomials, maybe a listening test will prove
this concern unjustified. since we need to track the signal envelope
anyway, the compression high-gain scenarios produce can be calculated
in the same stage.
so how many harmonics need to be generated?
FT'ing some high guitar notes shows that note attacks briefly contain
frequency content higher than 10 kHz, but the 'body' usually is far
below; the root of the highest note on the guitar is about 2.5 kHz.
if we're lucky, a few will do, with the lower harmonics masking the
upper, and the important thing the way they are weighted. brick-wall
lopass filtering of 'good' distortion will tell. if we're very
unlucky, we need a lot of them and may even need to oversample.
your thoughts?
tim
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