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

[pubpc1@library.ucla.edu]

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.