Re: Q: Applied Engineering Sound Card

[pubpc1@library.ucla.edu]

mjmahon@aol.com (MJMahon) wrote:
>Mitchell Spector (spec@vax2.concordia.ca) wrote:
>in response to my reply:
>>    Article? Well I do have an e-mail message from David Empson who
>>was explaining the technical details behind the low-pass filter, but
>>I don't want to post it without his permission. It certainly does
>>exist though, I've found references to the low-pass filter in some
>>Addison Wesley books and it should be covered in the Apple II technotes.
>>It definitely is not an advantage to have one. :/
>
>Wrong.  Sampling theory is quite clear on this point.  When any signal
>is recreated from discrete samples, there is no useful output above
>one-half the sampling frequency, the so-called Nyquist frequency.
>
>If energy above the Nyquist frequency is not filtered out, it will only
>increase the noise in the re-created waveform.  Think of it this way:
>the unfiltered output is a stairstep approximation to the sound being
>produced, while the desired sound is a continuous waveform (with
>maximum frequency not exceeding Sampling Freq./2).
>
>The same filtering must be applied prior to sampling an input waveform,
>since any energy above the Nyquist frequency would simply be "folded
>back" (aliased) into the frequency range from 0 to Nyquist freq.
>
>Since "brick wall" lowpass filters are hard to make and have undesirable
>phase-shift characteristics near the cutoff frequency, gentler lowpass
>filters are used, which will be 3db down somewhat before the Nyquist
>frequency, so that they can be >30db down at the Nyquist frequency
>(and beyond).
>
>Note that much lower lowpass cutoffs should be used when sampling
>at lower frequencies.  For example, if sampling at 11KHz, then the
>lowpass should cutoff lower than 5.5KHz, the Nyquist frequency.
>
>There ain't no such thing as a free lunch--and you can't do better
>than the Nyquist frequency!  A lowpass simply acknowledges
>reality and makes for a proper design.
>
>-michael


Michael, this finally makes some sense, both why the Amiga folks
claim their low-pass cutoff filter is an advantage and also why
the IIgs has one with a 26kHz cutoff.  Simply put, the maximum
sampling rate of the Ensoniq 5503 DOC, the sound chip of the GS,
appears to be (from my use of GS sound software) 56kHz.  With a
sampling rate of 52kHz, the Nyquist frequency would be 26kHz.  Thus,
by setting the lowpass to cutoff at 26kHz, Apple designers have
in fact followed proper design for a chip that can sample at 52kHz
(allowing a small discrepancy between 52kHz and 56kHz).

Similarly, for newer Macintosh computers which can sample at around
44.1kHz max, their cutoff filters should be around 22kHz (apparently
like the ones for the Amiga series).

-Scott G.