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: Jörn Nettingsmeier (nettings_AT_folkwang-hochschule.de)
Date: Tue Jan 29 2002 - 00:11:15 EET


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.

-- 
Jörn Nettingsmeier     
home://Kurfürstenstr.49.45138.Essen.Germany      
phone://+49.201.491621
http://spunk.dnsalias.org
http://www.linuxdj.com/audio/lad/


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