Re: Frequency response was Re: [linux-audio-user] Audiophile CD's

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Subject: Re: Frequency response was Re: [linux-audio-user] Audiophile CD's
From: Jason (hormonex_AT_yankthechain.com)
Date: Tue Jan 29 2002 - 00:34:36 EET


On Mon, 28 Jan 2002, [iso-8859-1] Jörn Nettingsmeier wrote:

> Jason wrote:
> >
> > On Mon, 28 Jan 28 you Ross wrote:
> > > > > Well, if a sound outside of my hearing range affects a sound inside my
> > > > > hearing range, I don't need to study the sound that was too high - if I
> > > > > could hear artifacts of the interaction, I can simply study the
> > > > > interaction.
> > > >
> > > > I was under the impression the resonant harmonics, artifacts etc. can be the
> > > > result of unheard as well as heard sonics interacting and that the playback
> > > > (percieved sound) of subsequent recording would suffer if that data was not
> > > > included with the recording or alter by adding it after the fact. similar to
> > > > the phono preamp mentioned earlier for the "vinyl warmth" effect.
> > >
> > > I'm not an acoustic enginner and I'm not a sampling theory expert. But this
> > > idea just doesn't jive with the way waveforms work. If the following analysis
> > > is wrong, someone _please_ correct it.
> > >
> > > Let's say I have some waveform A that I can hear, and some waveform B that is
> > > too high. Let's say that you are capable of identifying A (it's a simple 440Hz
> > > sine wave). Now, assume that sounding A and B together produces an audibly
> > > different sound. Since it is distinguishable from A, and B is inaudible, the
> > > tone of A and B must be a different waveform (call it C; it's equal to A+B).
> > > Since I can hear C, it must be below 22kHz. By the Nyquist Theorem I can sample
> > > this waveform at 44.1kHz and capture it completely.
> >
> > Close, hearing is actually kind of strange, and there are different parts
> > of our ears that pick up different frequencies in different ways. I'd like
> > to be able to explain that more clearly but it's a lot of Voodoo that I
> > don't have a very good understanding of.
> >
> > That having been said, the Nyquist theorem not only applies to
> > fundamentals, like A, but also to overtones like B. So if A is a
> > fundamental, and B is an overtone creating the composite waveform C, and
> > both a and b are are sub 22.05khz, then theoretically sampling at 44.1
> > will accurately
> > capture the frequency of both a and b, and therefore the correct frequency
> > and C. Timbre however, is a function of waveshape not frequency; the
> > closer a signal
> > gets to the Nyquist cutoff, the more generic it's shape becomes.
>
> true, but you needn't care. any "wave shape" other than plain sine
> means "additional overtones above the fundamental", because each and
> every shape can be expressed in terms of a sum of sine waves with
> different frequencies.
>
> a sawtooth wave for example is nothing else than a mix of f + 2f +
> 3f + 4f + 5f ... (where the amplitudes decrease as the factor gets
> higher. when you draw the graph, it will gradually begin to resemble
> a sawtooth, and it becomes less wobbly the more higher components
> you add.
>
> thus, their frequency is higher. you'll get all relevant overtones
> up to the 20something khz rolloff, but nothing higher, which you
> couldn't hear anyway.
>
>
hmmm. I'm really not convinced that hearing works by picking apart complex
waveforms into fundamentals. Can anyone recommend any good books on
psycho-acoustics that aren't *too* heavy on the calculus? If my thinking
is wrong on this, I really want to correct it.

-- 
YankTheChain.com - You can pretend we're not here. That's what I do.

,


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