Re: Why we have low pass filters, the Nyquist theorem (was Re: Expanding Focus Capacity)

[Frank Carney <frankc@cyberhighway.net>]

Makes sense to me.

pubpc1@library.ucla.edu wrote:

> Mitchell Spector wrote,
> in response to my reply:
> >>You must have not been paying attention, I'm saying it does
> >>not matter.  According to theory, you can capture a maximum
> >>frequency of 1/2 the sampling rate.  That means that even
> >>though a CD player is sampling at 44kHz, the maximum signal
> >>frequency it can carry is 22kHz.  What's above 22kHz is
> >>NOISE.  That 26kHz low pass filter is only filtering out
> >>NOISE.  You have to playback at 52kHz (double the 26kHz low
> >>pass filter) for the filter to have the effect you are
> >>thinking about.
> >
> >    So now there is no such thing is WYSIWYG, and there is
> >no difference between 22 kHz and 44 kHz. Uhuh. The way I
> >see things, your trying to make excuses about the graphic
> >and sound limitations of the GS so you can still compare
> >it favoribly to modern computers.
>
> Mitchell, you have not been paying attention.  I am just
> about to pull a Nathan Mates here!  Have you ever heard of
> the Nyquist theorem?  You haven't, have you?  Point your
> web browser to:
>
> http://www.opus1.com/~violist/help/nyquist.html
>
> and read that carefully.  Digest the information, now.  Do
> you see the explanation about the low pass filter.  Once
> again, here are the highlights of the Nyquist theorem and
> why we have low pass filters:
>
> The Nyquist Theorem:
> ----------------------------------------------------------------
>                   What about the high end?
>
> The sampling frequency determines the limit of audio frequencies
> that can be reproduced digitally. One of the most important rules
> of sampling is called the Nyquist Theorem, which states that the
> highest frequency which can be accurately represented is one-half
> of the sampling rate. So, if we want a full 20 kHz audio bandwidth,
> we must sample at least twice that fast, i.e. over 40 kHz. If we
> don't, bad things happen. Here's our example sine wave again:
> (see web page for graphic)
> ----------------------------------------------------------------
>
> Why we have low pass filters:
> ----------------------------------------------------------------
> (graphic of a mangled sine wave)
> Because of this, A/D converters must use lowpass filtering to
> remove all signals above the Nyquist frequency. Of course, it
> also means that in order to get high-fidelity sound, we have to
> take a lot of snapshots.
> ----------------------------------------------------------------
>
> Quick, Mitchell, what is the proper design of an A/D converter?
> Answer: "a low pass filter must be used to remove all signals
> above the Nyquist frequency."
>
> When a CD player samples at 44kHz, the objective is to capture
> 22kHz frequencies.  What is above 22kHz is NOISE.  CD players
> also have low pass filters that chop off the NOISE above the
> Nyquist frequency.  I _strongly_ suspect that if the designers
> of PC sound cards have any brains at all, most PC sound cards
> would also have low pass filtering.  Sure, it may be more
> advanced than that of the GS (I can imagine that their low pass
> filtering would sweep at 6kHz for 11kHz samples and 24kHz for
> 44kHz samples), but it is PROPER DESIGN to have one.  Otherwise,
> you get NOISE.
>
> >>First, sample a sound on your PC at 44kHz and 16 bit.
> >>Then sample the same sound at 44kHz and 8 bit.  Can you
> >>hear a difference?  Probably, but it is subtle.  Take
> >>the 44kHz 8 bit sound to the GS and play it.  There is
> >>absolutely no difference in quality between this playback
> >>and the playback of the PC (the 44kHz 8 bit one, that is).
> >
> >    So essential your trying to tell me sound or music recorded
> >at 16-bit, 44 kHz--and the same sound recorded at 8-bit, 22 kHz,
> >will sound more or less identical in quality?
>
> No. I am saying there is a subtle difference between 16-bit,
> 44kHz sound and 8-bit _44kHz_ sound.  Those kHz are the SAMPLING
> RATE!  Maximum frequency captured is _1/2_ the sampling rate.
> When your PC sound cards are sampling at 44kHz, only 22kHz of
> that is the maximum frequency capture.  What is above that is
> NOISE.  Most likely, your Roland is doing the right thing and
> taking out the noise above the NYQUIST FREQUENCY of 22kHz (or
> a little above that) with A LOW PASS FILTER.
>
> When you take the 8-bit 44kHz SAMPLE to the GS, the Ensoniq
> plays it as an 8-bit 44kHz SAMPLE.  Maximum frequency captured
> is _1/2_ the sampling rate.  What is above that is NOISE.  The
> sound gets CLEANED UP through the low pass filter.  You lose
> nothing compared to what you get when playing the same sound
> through the PC.
>
> Apple Computers may have done many things to hold back the GS,
> but the low pass filter was NOT one of them.
>
> >    Are you also saying the GS is closely comparable to a CD-player
> >for audio, is this what your claiming? If you are, then this debate
> >is starting is shift from a technical discussion to a comedic one.
>
> No.  However, the sound coming from a GS is quite good.  CD
> players have low pass filters, btw.
>
> I've worked out a system to get clean, long samples to the
> GS.  Digitize on a Mac or PC at 8-bit 44kHz.  Save and
> transfer on a Zip drive, hard drive, or null-modem over to
> an HFS volume on the GS (if using Zip drive with PC disk,
> use MUG!).  Use Longplay or Oversampler to play the sample.
> There's no loss in quality compared to playing the same
> sample on the PC.  The low pass filter is a good thing.
>
> -Scott G.